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 Work out a Rental Yield

How to Work out a Rental Yield.

Rental yield, essentially, tells you how much you can expect to earn from an investment property that you're renting out. It's typically expressed as a percentage of the cost of the property. You can use this figure to determine if a property you're thinking about buying would be a good investment or to understand your return on investment (ROI) in a property you already own. This figure is also helpful if you're trying to decide if a "buy-to-let" mortgage is affordable for you. To work out the rental yield, you need to know the total costs of buying and owning the property as well as the amount of rent you'll collect.

Method 1 Totaling Property Costs.
1. Calculate your yearly mortgage payments. If you have a mortgage on the property, total the mortgage payments you would make over the course of a year, including interest, taxes, and any associated fees. These payments are part of your cost of owning the property.
Even if you don't have a mortgage, you're likely still responsible for property taxes on the property. Those would also be considered part of your costs of ownership.
If you don't own the property yet, use an estimate of mortgage payments or get an offer from a mortgage company for the property and use that number instead.
2. Get a quote for insurance. If you rent out the property, you'll typically need landlord insurance, which may have different rates than homeowner's insurance. If you don't already own the property, a quote from a reputable insurer will help you estimate this cost.
In addition to landlord's insurance, you may also want to consider other types of insurance to cover damage to the property.
Rent insurance may also be available to you, which provides you some money in the event your tenant breaks their lease or needs to be evicted for nonpayment of rent.
3. Include any management fees or other property expenses. If you've hired a management company to run the property on your behalf, their fees are considered part of your costs. You may also have other property expenses or fees, depending on where the property is located.
For example, if you only own the building but not the land, you may have to pay rent for the land that the property sits on.
If you have a unit in an apartment building or condominium complex, you may also have association fees to consider.
Tip: Include in this category expenses you might incur in the event you have to advertise for a tenant. Fees for listing the property or doing background checks on tenants are also costs of owning and renting the property.
4. Estimate costs for repairs and maintenance. Over the course of the year, your tenant may have things break that need to be repaired. While you can't necessarily predict all of these expenses, you can typically come up with a reasonable estimate based on the age of the property and its fixtures.
You also want to consider major repairs that may be necessary in the event of a natural disaster or other event. While your insurance may cover some of this expense, you'll likely still have to pay a deductible.

Method 2 Determining Gross Rental Yield.
1. Total your yearly rental income. Evaluate how much you charge in rent, then multiply that amount to get the total rent you'll collect each year. If you collect weekly rent, multiply the weekly rent amount by 52. For monthly rent, multiply by 12.
For example, if you rent the property out for $500 a week, you would have an annual rental income of $26,000.
2. Find the current value of the property. If you plan to purchase the property this year, the value of the property would be equal to your purchase price. However, if you already own the property, use the most recent appraisal to determine the current value.
If you're looking at a property for sale, use the asking price as the value of the property, even if you think the asking price is too high and plan to make a lower bid on it.
3. Divide the rental income by the value to find the gross rental yield. Once you have those two figures, complete the equation. Your result will be a decimal value. Multiply that number by 100 to get a percentage.
For example, if your yearly rental income is $26,000 and the property is valued at $360,000, you have a gross rental yield of 7.2%. Gross rental yield is considered ideal if it's somewhere between 7 and 9%, so the gross rental yield for that property is good. Any lower than that, and you likely wouldn't have the cash flow in the event emergency repairs were needed.
Warning: While gross rental yield is easy to calculate, it doesn't take a lot of other factors into account that can affect the investment value of a property, such as the property's location, age, or condition.

Method 3 Calculating Net Rental Yield.
1. Start with your total yearly rental income. Just as when working out gross rental yield, you'll need the total rent you collect from the property in a year. Multiply weekly rent by 52 and monthly rent by 12 to find the annual amount.
For example, if you rented a condominium for $2,000 a month, your annual rental income would be $24,000.
Tip: Net rental yield is typically calculated at the end of the year, looking back at real numbers. If the property was vacant for any period during the year, don't include the rent you would have received for that time in your yearly rental income total.
2. Subtract your annual expenses from the rental income. For net rental yield, you'll also take into account the other costs of owning the property. Include all fees, mortgage payments, interest, taxes, insurance premiums, and other costs associated with the property for the year. Typically these will be monthly expenses, so don't forget to multiply them by 12 to get the annual total.
For example, suppose your annual rental income was $24,000 and the condominium unit cost you $900 a month to maintain. Your annual cost to own the property would be $10,800. When you subtract $10,800 from $24,000, you get $13,200.
3. Divide the result by the current value of the property. The current value of the property is not your mortgage payment, which likely includes interest, taxes, and other fees. Instead, look at the value of the most recent appraisal of the property. That's the amount you could likely sell the property for.
For example, suppose the condominium you own is worth $250,000. You have an annual rental income of $24,000 for the property, which decreased to $13,200 by the costs of owning the property. When you divide $13,200 by $250,000, you get 0.0528.
4. Multiply by 100 to find your net rental yield. Net rental yield, like gross rental yield, is expressed as a percentage of the value of the property. To get that percentage, take the decimal you got when you divided the annual rental income less costs by the current value of the property and multiply it by 100.
To continue the example, if you had annual rental income less costs of $13,200 divided by $250,000, you would have a net rental yield of 5.28%. This is considered a relatively low rental yield, but might still be sustainable depending on the location of the property or your reasons for owning it.

Community Q&A.

Question : When you say an acceptable yield is 7-9%, are you referring to the gross yield or the net yield?
Answer : A yield of 7 to 9% is considered a good yield regardless of whether it is a gross yield or a net yield. The net yield simply gives you more information about the actual cost of owning and managing the property. A property with a gross yield of 7 to 9% may have a much lower net yield, for example, if the property needed extensive renovations or repairs. In that case, it likely wouldn't be a worthwhile investment. However, a lower net yield might be acceptable depending on your reasons for owning the property and its location. For example, you might be willing to take a lower yield in a high-growth area where the property was rapidly appreciating in value.
Question : Does net yield include interest-only costs to the bank?
Answer : Net yield includes all costs of owning the property. If you have a mortgage on the property and are paying interest on that mortgage, those costs would be subtracted from your annual rental income along with all the other costs.
Question : What is the acceptable yield?
Answer : It depends on your goals. I'd say an acceptable average would be a 7-9% yield, but you may be happy taking as low as 4% if it's just supporting a pension, or if the property is located in an up-and-coming area where the value will increase significantly over time.
Question : Is there a good online calculator that will do this for me?
Answer : Excel or Google Docs can do this for you. Both are very good at it and keep track of it too. They both allow you to manipulate data to extract even more information.

Tips.

Work out your rental yield at least once a year. It will change depending on operating expenses and changes in the value of your property. Keeping tabs on your rental yield will help you determine when it's best to sell the property.
There are many real estate and finance companies that offer free rental yield calculators online. Simply search for "rental yield calculator" followed by the name of your country. The country name is necessary to ensure the calculator uses the same currency as you.

Warnings.

If you're comparing investment properties to buy, look at the property's past appreciation and potential to appreciate in the future as well as its rental yield. A high rental yield doesn't necessarily equate to a good investment if the property is in an undesirable area.

June 04, 2020