How to Use the Rule of 72

How to Use the Rule of 72.

The Rule of 72 is a handy tool used in finance to estimate the number of years it would take to double a sum of money through interest payments, given a particular interest rate. The rule can also estimate the annual interest rate required to double a sum of money in a specified number of years. The rule states that the interest rate multiplied by the time period required to double an amount of money is approximately equal to 72.
The Rule of 72 is applicable in cases of exponential growth, (as in compound interest) or in exponential "decay," as in the loss of purchasing power caused by monetary inflation.

Method 1 Estimating "Doubling" Time.
1. Let R x T = 72. R is the rate of growth (the annual interest rate), and T is the time (in years) it takes for the amount of money to double.
2. Insert a value for R. For example, how long does it take to turn $100 into $200 at a yearly interest rate of 5%? Letting R = 5, we get 5 x T = 72.
3. Solve for the unknown variable. In this example, divide both sides of the above equation by R (that is, 5) to get T = 72 ÷ 5 = 14.4. So it takes 14.4 years for $100 to double at an interest rate of 5% per annum. (The initial amount of money doesn't matter. It will take the same amount of time to double no matter what the beginning amount is.)
4. Study these additional examples:
How long does it take to double an amount of money at a rate of 10% per annum? 10 x T = 72. Divide both sides of the equation by 10, so that T = 7.2 years.
How long does it take to turn $100 into $1600 at a rate of 7.2% per annum? Recognize that 100 must double four times to reach 1600 ($100 → $200, $200 → $400, $400 → $800, $800 → $1600). For each doubling, 7.2 x T = 72, so T = 10. So, as each doubling takes ten years, the total time required (to change $100 into $1,600) is 40 years.

Method 2 Estimating the Growth Rate.
1. Let R x T = 72. R is the rate of growth (the interest rate), and T is the time (in years) it takes to double any amount of money.
2. Enter the value of T. For example, let's say you want to double your money in ten years. What interest rate would you need in order to do that? Enter 10 for T in the equation. R x 10 = 72.
3. Solve for R. Divide both sides by 10 to get R = 72 ÷ 10 = 7.2. So you will need an annual interest rate of 7.2% in order to double your money in ten years.

Method 3 Estimating Exponential "Decay" (Loss).
1. Estimate the time it would take to lose half of your money (or its purchasing power in the wake of inflation). Let T = 72 ÷ R. This is the same equation as above, just slightly rearranged. Now enter a value for R. An example.
How long will it take for $100 to assume the purchasing power of $50, given an inflation rate of 5% per year?
Let 5 x T = 72, so that T = 72 ÷ 5 = 14.4. That's how many years it would take for money to lose half its buying power in a period of 5% inflation. (If the inflation rate were to change from year to year, you would have to use the average inflation rate that existed over the full time period.)
2. Estimate the rate of decay (R) over a given time span: R = 72 ÷ T. Enter a value for T, and solve for R. For example.
If the buying power of $100 becomes $50 in ten years, what is the inflation rate during that time?
R x 10 = 72, where T = 10. Then R = 72 ÷ 10 = 7.2%.
3. Ignore any unusual data. If you can detect a general trend, don't worry about temporary numbers that are wildly out of range. Drop them from consideration.

Method 4 Derivation.
1. Understand how the derivation works for periodic compounding.
For periodic compounding, FV = PV (1 + r)^T, where FV = future value, PV = present value, r = growth rate, T = time.
If money has doubled, FV = 2*PV, so 2PV = PV (1 + r)^T, or 2 = (1 + r)^T, assuming the present value is not zero.
Solve for T by taking the natural logs on both sides, and rearranging, to get T = ln(2) / ln(1 + r).
The Taylor series for ln(1 + r) around 0 is r - r2/2 + r3/3 - ... For low values of r, the contributions from the higher power terms are small, and the expression approximates r, so that t = ln(2) / r.
Note that ln(2) ~ 0.693, so that T ~ 0.693 / r (or T = 69.3 / R, expressing the interest rate as a percentage R from 0-100%), which is the rule of 69.3. Other numbers such as 69, 70, and 72 are used for easier calculations.
2. Understand how the derivation works for continuous compounding. For periodic compounding with multiple compounding per year, the future value is given by FV = PV (1 + r/n)^nT, where FV = future value, PV = present value, r = growth rate, T = time, and n = number of compounding periods per year. For continuous compounding, n approaches infinity. Using the definition of e = lim (1 + 1/n)^n as n approaches infinity, the expression becomes FV = PV e^(rT).
If money has doubled, FV = 2*PV, so 2PV = PV e^(rT), or 2 = e^(rT), assuming the present value is not zero.
Solve for T by taking natural logs on both sides, and rearranging, to get T = ln(2)/r = 69.3/R (where R = 100r to express the growth rate as a percentage). This is the rule of 69.3.
For continuous compounding, 69.3 (or approximately 69) gives more accurate results, since ln(2) is approximately 69.3%, and R * T = ln(2), where R = growth (or decay) rate, T = the doubling (or halving) time, and ln(2) is the natural log of 2. 70 may also be used as an approximation for continuous or daily (which is close to continuous) compounding, for ease of calculation. These variations are known as rule of 69.3, rule of 69, or rule of 70.
A similar accuracy adjustment for the rule of 69.3 is used for high rates with daily compounding: T = (69.3 + R/3) / R.
The Eckart-McHale second order rule, or E-M rule, gives a multiplicative correction to the Rule of 69.3 or 70 (but not 72), for better accuracy for higher interest rate ranges. To compute the E-M approximation, multiply the Rule of 69.3 (or 70) result by 200/(200-R), i.e., T = (69.3/R) * (200/(200-R)). For example, if the interest rate is 18%, the Rule of 69.3 says t = 3.85 years. The E-M Rule multiplies this by 200/(200-18), giving a doubling time of 4.23 years, which better approximates the actual doubling time 4.19 years at this rate.
The third-order Padé approximant gives even better approximation, using the correction factor (600 + 4R) / (600 + R), i.e., T = (69.3/R) * ((600 + 4R) / (600 + R)). If the interest rate is 18%, the third-order Padé approximant gives T = 4.19 years.
To estimate doubling time for higher rates, adjust 72 by adding 1 for every 3 percentages greater than 8%. That is, T = [72 + (R - 8%)/3] / R. For example, if the interest rate is 32%, the time it takes to double a given amount of money is T = [72 + (32 - 8)/3] / 32 = 2.5 years. Note that 80 is used here instead of 72, which would have given 2.25 years for the doubling time.


FAQ.
Question : When would I need to use the rule of 72?
Answer : It's a handy shortcut when considering compounded, monetary gains or losses. For example, you might want to know how long it would take for invested money to double in value, given a specific rate of interest.
Question : How do I calculate compound interest?
Answer : The formula for annual compound interest (A) is: P [1 + (r / n)]^(nt), where P=principal amount, r = the annual interest rate as a decimal, n = the number of times the interest is compounded per year, and t = the number of years of the loan or investment.
Question : What is APY for an APR of 3.5% compounded?
Answer : It depends on how often the interest compounds: annually, semi-annually, quarterly, monthly or daily.

Tips.

Let the Rule of 72 work for you by starting to save now. At a growth rate of 8% a year (the approximate rate of return in the stock market), you would double your money in nine years (72 ÷ 8 = 9), quadruple your money in 18 years, and have 16 times your money in 36 years.
The value of 72 was chosen as a convenient numerator in the above equation. 72 is easily divisible by several small numbers: 1,2,3,4,6,8,9, and 12. It provides a good approximation for annual compounding at typical rates (from 6% to 10%). The approximations are less exact at higher interest rates.
You can use Felix's Corollary to the Rule of 72 to calculate the "future value" of an annuity (that is, what the annuity's face value will be at a specified future time). You can read about the corollary on various financial and investing websites.

Warnings.
Let the rule of 72 convince you not to take on high-interest debt (as is typical with credit cards). At an average interest rate of 18%, semiretired credit card debt doubles in just four years (72 ÷ 18 = 4), quadruples in eight years, and becomes completely unmanageable after that.

April 10, 2020

How to Calculate Finance Charges on a Leased Vehicle

How to Calculate Finance Charges on a Leased Vehicle.

At some point, you may want or need to have a new car. You may also want to weigh the cost differences between leasing and buying before you make your decision. One way to compare costs is to figure out exactly what you will be paying for each. When you buy a car, you finance the amount charged for the vehicle and the interest rate is clear. When you lease a car, you pay to use the vehicle for a period of time, similar to renting it, and turn it in at the end of the lease. The finance charges for a lease may not always be clear. To calculate the finance charges on a leased vehicle, you need to know only a few things: the net capitalized cost, residual value and money factor. If these are known, calculating your finance charges is a simple process.

Part 1 Collecting Necessary Data.

1. Determine the net cap cost. The term “net cap cost” is a shortened form of net capitalized cost. This is ultimately the overall price of the vehicle. The net cap cost may be affected by other additions or subtractions, as follows.

Any miscellaneous fees or taxes are added to the cost to increase the net cap cost.

Any down payment, trade in or rebates are considered “net cap reductions.” These are subtracted and will reduce the net cap cost.

Suppose, for example, that a vehicle is listed with a cost of $30,000. There is a rebate or you make a down payment of $5,000. Therefore, the net cap cost for this vehicle is $25,000.

2. Establish the residual value of the vehicle. This is a bit like predicting the future. The residual value is the vehicle’s value at the end of the lease, when you will return it. This is always a bit uncertain because nobody can predict the exact condition of the vehicle, the mileage or the repairs that it will undergo during the lease. To establish the residual value, dealers use industry guide books, such as the Automotive Leasing Guide (ALG).

The graphic shown above illustrates the decline in the vehicle’s value over time. For this example, the residual value at the end of the term is set at $15,000.

Some dealers choose not to use the ALG. Instead, they may develop their own guide or functions for setting residual values.

3. Find out the dealer’s money factor. Leased vehicles do not charge interest in the same way that purchase agreements do. There is, however, a finance charge that is analogous to interest. You are paying the leasing company for the use of their vehicle during the term of your lease. This charge is based on a number called the “money factor.”

The money factor is not generally publicized. You will need to ask the dealer to share it with you.

The money factor does not look like an interest rate. It will generally be a decimal number like 0.00333. To compare the money factor to an annual interest rate, multiply the money factor by 2400. In this example, a money factor of 0.00333 is roughly like a loan interest rate of 0.00333x2400 = 7.992% interest. This is not an exact equivalence but is a regularly accepted comparison value.

Part 2 Performing the Calculations.

1. Add the net cap cost and the residual value. The finance charge is based on the sum of the net cap cost and the residual value. At first glance, this appears to be an unfair doubling of the car’s value. However, in combination with the money factor, this works as a way to average the net cap cost and the residual value. You end up paying the finance fee on an average overall value of the car.

Consider the example started above. The net cap cost is $25,000, and the residual is $15,000. The total, therefore, is the sum of $25,000+$15,000 = $40,000.

2. Multiply that sum by the money factor. The money factor is applied to the sum of the net cap cost and the residual value of the car to find the monthly finance charge.

Continuing with the example above, use the money factor 0.00333. Multiply this by the sum of the net cap cost and residual as follows:

$40,000 x 0.00333 = $133.2.

3. Apply the monthly finance charge. The result of the final calculation is the monthly finance charge that will be added to your lease payment. In this example, the finance charge is $133.20 each month.

4. Figure the full monthly payment. The finance charge may be the largest portion of your monthly payment, but you cannot count on it to be the full payment. In addition to the finance charge, many dealers will also charge a depreciation fee. This is the cost that you pay to compensate the dealer for the decreased value of the car over time. Finally, you may be responsible for assorted taxes.

Before you sign any lease agreement, you should find out the full monthly charge you are responsible for. Ask the dealer to itemize all the costs for you, and make sure that you understand and can afford them all.

Part 3 Negotiating with the Dealer.

1. Ask for the data you want. Many people, when leasing a vehicle, seem satisfied to accept the bottom line figure that the dealer assigns. However, to verify that any deal you negotiate is actually honored, you need to know the details of the finance charge calculations. Without asking for the data, you could be the victim of carelessness, simple error, or even fraud.

You could negotiate a reduced price for the vehicle, but then the dealer could base the calculations on the original value anyway.

The dealer might not apply proper credit for a trade-in vehicle.

The dealer could make mathematical errors in calculating the finance charge.

The dealer could apply a money factor other than the one used in the original negotiations.

2. Press the dealer for the “money factor.” The money factor is a decimal number that car dealerships use to calculate the finance charges. This number is not an interest rate but is somewhat analogous to interest rates. Some lease dealers may publicize the money factor, while others may not. You should ask for the money factor that your dealer is using. Also ask how the money factor is used to calculate the finance fee charged on your lease.

3. Ask the dealer to show you the calculation worksheet. The dealer is not required to share with you the calculations that go into the finance charge and monthly payments on your leased vehicle. Unless you ask specifically, you will probably never see that information. You should ask the dealer, sales clerk or manager to share the calculations with you. Even if you have the individual bits of data, you may not be able to confirm that the figures were calculated accurately or fairly unless you compare your notes to the dealer’s calculations.

4. Threaten to leave if the dealer is not forthcoming with information. The only leverage you have in the negotiations over a leased vehicle’s finance charges is the ability to walk away. Make it clear to the dealer that you want to verify the calculations and the individual pieces of information that go into figuring your finance charges. If the dealer is unwilling to share this information with you, you should threaten to leave and lease your car from somewhere else.

Tips.

If the lease dealership will not provide you with the money factor, go to a different dealer. You cannot determine and compare your true costs and fair value unless you have this information.

The higher the car value at lease end (that is, less depreciation), the less your finance charges will be, which, in turn, will reduce your monthly payment.

Warnings

Some dealers may present the money factor number so that it is easier to read, such as 3.33; however, this could be misinterpreted as the interest rate. Be aware that this is not the rate that will be used. This number should be converted to the actual money factor by dividing by 1,000 (3.33 divided by 1,000 = 0.00333).

Be aware that the finance cost (as calculated here to be $133.20) is not necessarily your total monthly payment. It is only the finance charge and may not include other charges such as sales tax or the acquisition fee.

Things You'll Need : Net cap cost, Residual cost, Money factor, Paper, Pen or pencil, Calculator.

December 19, 2019

how to calculate finance charges on a leased vehicle

How to Calculate Finance Charges on a Leased Vehicle.

At some point, you may want or need to have a new car. You may also want to weigh the cost differences between leasing and buying before you make your decision. One way to compare costs is to figure out exactly what you will be paying for each. When you buy a car, you finance the amount charged for the vehicle and the interest rate is clear. When you lease a car, you pay to use the vehicle for a period of time, similar to renting it, and turn it in at the end of the lease. The finance charges for a lease may not always be clear. To calculate the finance charges on a leased vehicle, you need to know only a few things: the net capitalized cost, residual value and money factor. If these are known, calculating your finance charges is a simple process.

Part 1 Collecting Necessary Data.

1. Determine the net cap cost. The term “net cap cost” is a shortened form of net capitalized cost. This is ultimately the overall price of the vehicle. The net cap cost may be affected by other additions or subtractions, as follows.

Any miscellaneous fees or taxes are added to the cost to increase the net cap cost.

Any down payment, trade in or rebates are considered “net cap reductions.” These are subtracted and will reduce the net cap cost.

Suppose, for example, that a vehicle is listed with a cost of $30,000. There is a rebate or you make a down payment of $5,000. Therefore, the net cap cost for this vehicle is $25,000.

2. Establish the residual value of the vehicle. This is a bit like predicting the future. The residual value is the vehicle’s value at the end of the lease, when you will return it. This is always a bit uncertain because nobody can predict the exact condition of the vehicle, the mileage or the repairs that it will undergo during the lease. To establish the residual value, dealers use industry guide books, such as the Automotive Leasing Guide (ALG).

The graphic shown above illustrates the decline in the vehicle’s value over time. For this example, the residual value at the end of the term is set at $15,000.

Some dealers choose not to use the ALG. Instead, they may develop their own guide or functions for setting residual values.

3. Find out the dealer’s money factor. Leased vehicles do not charge interest in the same way that purchase agreements do. There is, however, a finance charge that is analogous to interest. You are paying the leasing company for the use of their vehicle during the term of your lease. This charge is based on a number called the “money factor.”

The money factor is not generally publicized. You will need to ask the dealer to share it with you.

The money factor does not look like an interest rate. It will generally be a decimal number like 0.00333. To compare the money factor to an annual interest rate, multiply the money factor by 2400. In this example, a money factor of 0.00333 is roughly like a loan interest rate of 0.00333x2400 = 7.992% interest. This is not an exact equivalence but is a regularly accepted comparison value.

Part 2 Performing the Calculations.

1. Add the net cap cost and the residual value. The finance charge is based on the sum of the net cap cost and the residual value. At first glance, this appears to be an unfair doubling of the car’s value. However, in combination with the money factor, this works as a way to average the net cap cost and the residual value. You end up paying the finance fee on an average overall value of the car.

Consider the example started above. The net cap cost is $25,000, and the residual is $15,000. The total, therefore, is the sum of $25,000+$15,000 = $40,000.

2. Multiply that sum by the money factor. The money factor is applied to the sum of the net cap cost and the residual value of the car to find the monthly finance charge.

Continuing with the example above, use the money factor 0.00333. Multiply this by the sum of the net cap cost and residual as follows:

$40,000 x 0.00333 = $133.2.

3. Apply the monthly finance charge. The result of the final calculation is the monthly finance charge that will be added to your lease payment. In this example, the finance charge is $133.20 each month.

4. Figure the full monthly payment. The finance charge may be the largest portion of your monthly payment, but you cannot count on it to be the full payment. In addition to the finance charge, many dealers will also charge a depreciation fee. This is the cost that you pay to compensate the dealer for the decreased value of the car over time. Finally, you may be responsible for assorted taxes.

Before you sign any lease agreement, you should find out the full monthly charge you are responsible for. Ask the dealer to itemize all the costs for you, and make sure that you understand and can afford them all.

Part 3 Negotiating with the Dealer.

1. Ask for the data you want. Many people, when leasing a vehicle, seem satisfied to accept the bottom line figure that the dealer assigns. However, to verify that any deal you negotiate is actually honored, you need to know the details of the finance charge calculations. Without asking for the data, you could be the victim of carelessness, simple error, or even fraud.

You could negotiate a reduced price for the vehicle, but then the dealer could base the calculations on the original value anyway.

The dealer might not apply proper credit for a trade-in vehicle.

The dealer could make mathematical errors in calculating the finance charge.

The dealer could apply a money factor other than the one used in the original negotiations.

2. Press the dealer for the “money factor.” The money factor is a decimal number that car dealerships use to calculate the finance charges. This number is not an interest rate but is somewhat analogous to interest rates. Some lease dealers may publicize the money factor, while others may not. You should ask for the money factor that your dealer is using. Also ask how the money factor is used to calculate the finance fee charged on your lease.

3. Ask the dealer to show you the calculation worksheet. The dealer is not required to share with you the calculations that go into the finance charge and monthly payments on your leased vehicle. Unless you ask specifically, you will probably never see that information. You should ask the dealer, sales clerk or manager to share the calculations with you. Even if you have the individual bits of data, you may not be able to confirm that the figures were calculated accurately or fairly unless you compare your notes to the dealer’s calculations.

4. Threaten to leave if the dealer is not forthcoming with information. The only leverage you have in the negotiations over a leased vehicle’s finance charges is the ability to walk away. Make it clear to the dealer that you want to verify the calculations and the individual pieces of information that go into figuring your finance charges. If the dealer is unwilling to share this information with you, you should threaten to leave and lease your car from somewhere else.

Tips.

If the lease dealership will not provide you with the money factor, go to a different dealer. You cannot determine and compare your true costs and fair value unless you have this information.

The higher the car value at lease end (that is, less depreciation), the less your finance charges will be, which, in turn, will reduce your monthly payment.

Warnings

Some dealers may present the money factor number so that it is easier to read, such as 3.33; however, this could be misinterpreted as the interest rate. Be aware that this is not the rate that will be used. This number should be converted to the actual money factor by dividing by 1,000 (3.33 divided by 1,000 = 0.00333).

Be aware that the finance cost (as calculated here to be $133.20) is not necessarily your total monthly payment. It is only the finance charge and may not include other charges such as sales tax or the acquisition fee.

Things You'll Need : Net cap cost, Residual cost, Money factor, Paper, Pen or pencil, Calculator.

December 19, 2019

How to Calculate Finance Charges on a New Car Loan

How to Calculate Finance Charges on a New Car Loan.

While some people save until they can buy a car in full, most people take out a car loan. This makes newer and better cars more accessible to everyone. However, it also makes car ownership even more expensive in the long run. Before taking out a loan, you should consider the additional money you will pay in interest for the duration of your loan. These payments, also known as finance charges, will be included in your payments and can be calculated either as monthly payments or as a sum total over the life of your loan.

Part 1 Clarifying the Terms of Your Loan.

1. Determine how much you will borrow. Typically, buyers will make a cash down payment on their new car and borrow from a lender to cover the remaining cost. This borrowed amount, known as the principal, will serve as the basis for your car loan. Keep in mind that you should put as much money down on your car as possible to minimize the amount borrowed and reduce your finance charges.

This step will require you to know roughly how much your new car will cost. See How to Buy a New Car for more information about finding a good price and working within your budget.

2. Figure out the annual percentage rate (APR) and duration of your loan. The APR reflects how much additional money you will have to pay beyond your principal for each year of your loan. A low APR will reduce the yearly and monthly amounts of finance charges on your loan. However, many low-APR loans are longer in duration, so the overall cost may remain relatively high. Alternately, a short-term loan with a higher APR may end up being cheaper overall. This is why it is important to calculate your finance charges beforehand.

Getting a low APR on your car loan may mean seeking other lenders beyond your car dealership. Be sure to do your research and select the cheapest available combination of APR and duration. See How to Get a Low APR on a Car Loan for more information.

3. Find out how many payments you will make each year. The majority of car loan payments are made on a monthly basis. When calculating your monthly payments, you will need to know both how many payments you will make each year and how many payments you will make in total. This information can be easily found in the terms of your car loan.

Part 2 Calculating Your Monthly Finance Charges.

1. Save time by using an online calculator. There are many car loan payment calculators available for free online. Take advantage of these free services if you don't want to spend the time calculating your payments yourself. Search "Car loan payment calculator" and you will be provided with many options. If you still want to work it out by hand, continue to the next step.

2. Find your interest rate due on each payment. Start by converting your APR to a decimal by dividing it by 100. For example, if your APR is stated at 8.4%, 8.4/100 = 0.084. Next, find your monthly percentage rate by dividing your APR decimal by 12. So, 0.084/12 = 0.007. This is your monthly percentage rate expressed as a decimal.

3. Multiply your monthly percentage rate times your principal. If, for example, your principal were $20,000 (if you borrowed $20,000 to buy your car), you would multiply this by 0.007 (from the previous step) and get 140.

4. Input this number into the monthly payment formula. The formula is as follows: Monthly Payment = (Interest rate due on each payment x principal)/ (1 – (1 + Interest rate due on each payment)^ -(Number of payments)). The top part of the equation (interest rate due on each payment x principal) is your number from the previous step. The rest can be calculated using a simple calculator.

The "^" indicates that the figure (-(Number of Payments)) is an exponent to the figure (1 + Interest rate due on each payment). On a calculator, this is entered by calculating 1 + interest rate due on each payment, hitting the button x^y, and then entering the number of payments. Keep in mind that the number of payments is made negative here (multiplied by negative one).

In our example, the calculation would go as follows (assuming a loan duration of 5 years or 60 months):

Monthly Payment = (0.007 x $20000)/(1-(1+ 0.007)^-60.

Monthly payment = $140/(1-(1.007)^-60).

Monthly payment = $140/(1-0.658).

Monthly payment = $140/0.342.

Monthly payment = $409.36 (this number may be off by a few cents due to rounding).

5. Calculate the amount of principal paid each month. This is done by simply dividing your principal amount by the duration of your loan in months. For our example, this would be $20,000/60 months = $333.33/month.

6. Subtract your principal paid each month from your monthly payment. In our example, this would be $409.36 - $333.33. This equals roughly $76. So, with this loan agreement, you would be spending $76 per month in interest payments alone.

Part 3 Calculating Your Loan's Total Finance Charges.

1. Find your monthly payment. To find your total finance charges over the life of your loan, start by calculating your monthly payment. How to do this is explained in the previous section.

2. Plug that number into the total finance charges formula. The formula is as follows: Monthly Payment Amount x Number of Payments – Amount Borrowed = Total Amount of Finance Charges.

So, in our example, this would be.

$409 x 60 - $20,000 = Total amount of finance charges.

$24,540 - $20,000 = Total amount of finance charges.

Total amount of finance charges = $4,540.

3. Check your work. To be sure that you calculated your total correctly, divide that number by the total number of payments (60, in this case). $4,540/60 = 76. If the result matches your monthly finance charges you calculated earlier, then you have the correct number for total finance charges.

Tips.

Use this process to compare loan plans to ensure that you end up with the lowest possible value for overall finance charges.

Using an online loan calculator will always be simpler and more convenient than working out the numbers on your own. These online calculators are always accurate.

The calculator included on most smartphones is capable of doing the math here. If you don't have a smart phone or calculator to use, try typing your equation into Google's search bar, as it will solve most simple problems.

With good credit and a large down payment, it may be possible to get a car loan with 0% APR.

Warnings.

While uncommon, some lenders can use a more complicated form of interest called compound interest that will throw off these calculations. Be sure to ask if your car loan charges simple interest (the kind described in this article) before counting on these equations.

November 28, 2019

how to calculate finance charges on a new car loan

How to Calculate Finance Charges on a New Car Loan.

While some people save until they can buy a car in full, most people take out a car loan. This makes newer and better cars more accessible to everyone. However, it also makes car ownership even more expensive in the long run. Before taking out a loan, you should consider the additional money you will pay in interest for the duration of your loan. These payments, also known as finance charges, will be included in your payments and can be calculated either as monthly payments or as a sum total over the life of your loan.

Part 1 Clarifying the Terms of Your Loan.

1. Determine how much you will borrow. Typically, buyers will make a cash down payment on their new car and borrow from a lender to cover the remaining cost. This borrowed amount, known as the principal, will serve as the basis for your car loan. Keep in mind that you should put as much money down on your car as possible to minimize the amount borrowed and reduce your finance charges.

This step will require you to know roughly how much your new car will cost. See How to Buy a New Car for more information about finding a good price and working within your budget.

2. Figure out the annual percentage rate (APR) and duration of your loan. The APR reflects how much additional money you will have to pay beyond your principal for each year of your loan. A low APR will reduce the yearly and monthly amounts of finance charges on your loan. However, many low-APR loans are longer in duration, so the overall cost may remain relatively high. Alternately, a short-term loan with a higher APR may end up being cheaper overall. This is why it is important to calculate your finance charges beforehand.

Getting a low APR on your car loan may mean seeking other lenders beyond your car dealership. Be sure to do your research and select the cheapest available combination of APR and duration. See How to Get a Low APR on a Car Loan for more information.

3. Find out how many payments you will make each year. The majority of car loan payments are made on a monthly basis. When calculating your monthly payments, you will need to know both how many payments you will make each year and how many payments you will make in total. This information can be easily found in the terms of your car loan.

Part 2 Calculating Your Monthly Finance Charges.

1. Save time by using an online calculator. There are many car loan payment calculators available for free online. Take advantage of these free services if you don't want to spend the time calculating your payments yourself. Search "Car loan payment calculator" and you will be provided with many options. If you still want to work it out by hand, continue to the next step.

2. Find your interest rate due on each payment. Start by converting your APR to a decimal by dividing it by 100. For example, if your APR is stated at 8.4%, 8.4/100 = 0.084. Next, find your monthly percentage rate by dividing your APR decimal by 12. So, 0.084/12 = 0.007. This is your monthly percentage rate expressed as a decimal.

3. Multiply your monthly percentage rate times your principal. If, for example, your principal were $20,000 (if you borrowed $20,000 to buy your car), you would multiply this by 0.007 (from the previous step) and get 140.

4. Input this number into the monthly payment formula. The formula is as follows: Monthly Payment = (Interest rate due on each payment x principal)/ (1 – (1 + Interest rate due on each payment)^ -(Number of payments)). The top part of the equation (interest rate due on each payment x principal) is your number from the previous step. The rest can be calculated using a simple calculator.

The "^" indicates that the figure (-(Number of Payments)) is an exponent to the figure (1 + Interest rate due on each payment). On a calculator, this is entered by calculating 1 + interest rate due on each payment, hitting the button x^y, and then entering the number of payments. Keep in mind that the number of payments is made negative here (multiplied by negative one).

In our example, the calculation would go as follows (assuming a loan duration of 5 years or 60 months):

Monthly Payment = (0.007 x $20000)/(1-(1+ 0.007)^-60.

Monthly payment = $140/(1-(1.007)^-60).

Monthly payment = $140/(1-0.658).

Monthly payment = $140/0.342.

Monthly payment = $409.36 (this number may be off by a few cents due to rounding).

5. Calculate the amount of principal paid each month. This is done by simply dividing your principal amount by the duration of your loan in months. For our example, this would be $20,000/60 months = $333.33/month.

6. Subtract your principal paid each month from your monthly payment. In our example, this would be $409.36 - $333.33. This equals roughly $76. So, with this loan agreement, you would be spending $76 per month in interest payments alone.

Part 3 Calculating Your Loan's Total Finance Charges.

1. Find your monthly payment. To find your total finance charges over the life of your loan, start by calculating your monthly payment. How to do this is explained in the previous section.

2. Plug that number into the total finance charges formula. The formula is as follows: Monthly Payment Amount x Number of Payments – Amount Borrowed = Total Amount of Finance Charges.

So, in our example, this would be.

$409 x 60 - $20,000 = Total amount of finance charges.

$24,540 - $20,000 = Total amount of finance charges.

Total amount of finance charges = $4,540.

3. Check your work. To be sure that you calculated your total correctly, divide that number by the total number of payments (60, in this case). $4,540/60 = 76. If the result matches your monthly finance charges you calculated earlier, then you have the correct number for total finance charges.

Tips.

Use this process to compare loan plans to ensure that you end up with the lowest possible value for overall finance charges.

Using an online loan calculator will always be simpler and more convenient than working out the numbers on your own. These online calculators are always accurate.

The calculator included on most smartphones is capable of doing the math here. If you don't have a smart phone or calculator to use, try typing your equation into Google's search bar, as it will solve most simple problems.

With good credit and a large down payment, it may be possible to get a car loan with 0% APR.

Warnings.

While uncommon, some lenders can use a more complicated form of interest called compound interest that will throw off these calculations. Be sure to ask if your car loan charges simple interest (the kind described in this article) before counting on these equations.

November 28, 2019