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Rule of 72 Definition

Rule of 72 Definition

The rule of 72 definition is an approximation tool used to determine the amount of time it will take for money to double on the earnings of compound interest. The Rule of 72 is also used to calculate the rate of return necessary to double an investment in a specific amount of years.

Rule of 72 Explained

The rule of 72 is essentially an estimation for determining the amount of years or the doubling time of an investment. This is done by taking the interest available on the investment and dividing it by 72. Rule of 72 investing is usually fairly accurate. It is even more accurate with lower interest rates than it is for higher ones. Use he rule of 72 for compound interest situations. If the investment earns a simple interest at the end of the investment term, then this rule is not a very good indicator. The rule of 72 is most useful if an investor cannot perform an exponential function and simply needs to do simple math for an estimate of an investment.

A lower compound interest rate means that the investment will take longer to double. Whereas, a higher interest rate means that the investment will be doubled quicker. Thus, a higher interest rate and a lower doubling time are necessary for an investment to grow faster. Usually, a riskier investment will yield a higher interest rate and a higher return in less time. If you are planning on saving or investing your funds, then it is important for you to compare different interest rates so that you can maximize the value of your investment in the shortest amount of time. Since the rate of returns for investments vary with time, use the Rule of 72 as a quick tool. But do not use it as a full solution for analyzing the future value of investments.

Rule of 72 Formula

The rule of 72 formula is as follows:

Doubling Time (# years) = 72/Interest Rate

Rule of 72 Example

What is the doubling time for an investment with a compound interest rate of 8%? A person using the rule of 72 equation would find the doubling time equal to 9 years. Calculate this by taking 72 and dividing it by 8. By performing this the investor can tell that it will take approximately 9 years to double the principal. It is fairly accurate as the exponential function yields an actual doubling time of 9.006 years. If you want to calculate the interest rate necessary to double your funds for a specific number of years, then divide 72 by the doubling time (# years).

 

Rule of 72 Definition

 

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What is Compound Interest?

See Also:
Effective Rate of Interest Calculation
When is Interest Rate Not as Important in Selecting a Loan?
Interest Expense
Nominal Interest Rate
Interest Rate Swaps

What is Compound Interest?

Compound interest is interest earned on the principal plus interest earned on prior interest. Compounding interest rates not only earn interest on the original money, but also on the interest itself. The interest earns interest. Or, as Benjamin Franklin put it, “The money that money makes, makes money.”

For example, if an investor invests $100 at a 10% interest rate compounded yearly, during the first year the investment would earn interest on the original $100, and the next year the investment would earn interest on the original $100 plus the $10 of interest earned in the prior year.


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Compounding Periods

You can compound compound interest at different intervals, such as yearly, semi-annually, quarterly, monthly, daily, or continuously.

For yearly compounding interest rates, the original capital earns interest at the stated annual rate over the course of the year. The following year, the interest earned during the first year is added to the original capital, and the investment earns interest on the new amount.

For semi-annual, quarterly, monthly, or daily compounding interest rates, the original capital earns interest for the stated time period. At the end of that stated time period, the interest earned is added to the capital, and for the next period interest is earned on that new amount. This continues and the amount of money that earns interest gets larger and larger each period.

For a continuously compounding rate, the compounding period is an instant. In this case, compound the interest an infinite number of times during the course of a year.

Compound Interest and Simple Interest

There is a difference between compound interest and simple interest. An investment with compound interest grows faster than an investment with simple interest. Simple interest is interest earned on the original amount of capital. Each time period, the stated interest rate applies only to the principal amount. With simple interest, the interest itself does not earn interest.

For example, if $100 is invested at 10% yearly simple interest rate, then the investment earns $10 of interest each year. Each year, the interest rate applies only to the original $100 dollars and not to the accumulating interest.

Compound interest, as stated above, earns interest on the principal as well as the interest earned in prior periods. For example, if an investor invests $100 at a 10% interest rate compounded yearly, during the first year the investment would earn interest on the original $100, and the next year the investment would earn interest on the original $100 plus the $10 of interest earned in the prior year.

Compound Interest Formula

Here is how you calculate the value of an investment with compound interest after a certain number of years. First, divide the annual interest rate by the number of compounding periods. Then add one to that number. Next raise that value to the product of the number of compounding periods multiplied by the number of years of the investment. Take the value, and multiply it by the principal value. This gives you the ending value of the investment including compounded interest.

Investment Value = Principal x (1 + (Annual Rate/Periods))periods x years

Compound Interest Monthly Formula

Use the following formula to calculate compound interest on a monthly basis:

Investment Value = Principal x (1 + (Annual Rate/12))12

For example, if you invest $100 at an annual rate of 6% that compounds monthly, then at the end of one year, the value of the investment would be $106.17.

$106.17 = $100 x (1 + (.06/12))12

Compound Interest Formula Quarterly

Use the following formula to calculate compound interest on a quarterly basis:

Investment Value = Principal x (1 + (Annual Rate/4))4

For example, if you invest $100 at an annual rate of 6% that compounds quarterly, then at the end of one year, the value of the investment would be $106.14.

$106.14 = $100 x (1 + (.06/4))4

compound interest

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Rule of 72

The rule of 72 is an approximation tool used to determine the amount of time it will take for money to double on the earnings of compound interest.

Rule of 72 Explained

The rule of 72 is essentially an estimation for determining the amount of years or the doubling time of an investment. Do this by taking the interest available on the investment. Then divide it by 72. This type of investing is usually fairly accurate, it is more accurate with lower interest rates than it is for higher ones. It is normally used solely for compound interest situations and is not a very good indicator if the investment earns a simple interest at the end of the investment term. This rule is most useful if an investor cannot perform an exponential function and simply needs to do simple math for an estimate of an investment.

Rule of 72 Formula

Use the following rule of 72 formula:

Doubling Time (# years) = 72/Interest Rate

Example

What is the doubling time for an investment with a compound interest rate of 8%? A person using the rule of 72 equation would find the doubling time equal to 9 years. Calculate it by dividing 8 by 72. By performing this, the investor can tell that it will take approximately 9 years to double the principal. It is fairly accurate as the exponential function yields an actual doubling time of 9.006 years.

rule of 72

See Also:
Investment Banks
NPV vs Payback Method
Internal Rate of Return Method
Weighted Average Cost of Capital (WACC)
Effective Rate of Interest Calculation

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Interest Rate Definition

See Also:
Effective Rate of Interest Calculation
Interest Expense
What are the 7 Cs of banking
Time Value of Money (TVM)
Interest Rate Risk
LIBOR vs Prime Rate
Federal Funds Rate Definition
Treasury Inflation Protected Securities

Interest Rate Definition

An interest rate signifies a borrowing cost. The interest rate definition is the rate the lender charges the borrower for the use of money. Quote interest rates as annual rates, which represent a percentage of the borrowed principal. Interest rates are used in all types of business and consumer loans, including auto loans, mortgages, credit cards, and any other contract that involves a borrower and a lender. A borrower with good credit – and therefore less risk of default – can borrow money at a lower rate than a borrower with poor credit.

Benchmark Interest Rates

Business and consumer loans, as well as interest rate derivatives (see below), often rely on benchmark interest rates, such as the fed funds rate, the prime rate, Libor, or U.S. Treasury rates. For example, a company may borrow money from a commercial bank at a rate equal to the prime rate plus a specified quoted margin. The quoted margin, or spread between the benchmark rate and the interest rate used in the loan, would depend on the credit standing of the borrower.

Interest Rate Derivatives

Furthermore, interest rates are also frequently used in financial derivatives, such as interest rate futures and interest rate swaps. With financial derivatives, the value of the derivative instrument depends on fluctuations in the underlying interest rate.

Calculate Interest on Loan

Use the following equations to calculate interest on a loan:

Simple Interest = Principal x Interest Rate x Time Periods

Compound Interest = Principal x (((1 + Interest Rate)^Time Periods) – 1)

Interest Payment = Principal x Interest Rate

Principal = Interest Payment / Interest Rate

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Interest rate definition

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Interest rate definition

 

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Future Value

See Also:
Valuation Methods
Net Present Value Method
Adjusted Present Value (APV) Method
Present Value (PV)
Opportunity Cost

Future Value Definition

Future value (FV) is the value of a sum of money at a future point in time for a given interest rate. The idea is to adjust the present value of a sum of money for the time value of money over the specified time period.

If the present value is $1.00, and the interest rate is 10%, then the FV of that dollar one year from now would be $1.10. If someone offered you a dollar now or a dollar one year from now, you’d prefer the dollar now. Because by taking the dollar now and investing it, it will be worth more than one dollar a year from now. By applying that same concept to larger quantities of money, you can see that money now is more valuable than the same amount of money later and that it is necessary to consider the time value of money when making financial decisions.

Future value can be calculated with simple interest or compound interest. Practically speaking, it is more useful to calculate future value using compound interest. Simple interest accounts for interest accumulation over time without compounding. It is simply the principal amount adjusted for the annual interest rate. Compound interest accounts for the interest earned on the value of previous interest earned.

Future Value Formula for Simple Interest

FV = Present Value x (1 + (Interest Rate x Time Periods))

One dollar at 10% for one year: $1.10 = $1.00 x (1 + (.10 x 1))

One dollar at 10% for five years: $1.50 = $1.00 x (1 + (.10 x 5))

Future Value Formula for Compound Interest

FV = Present Value x (1 + Interest Rate) Time Periods

One dollar at 10% for one year: $1.10 = $1.00 x (1 + .10)1

One dollar at 10% for five years: $1.61 = $1.00 x (1 + .10)5

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Future Value Definition, Future Value Formula for Simple Interest, Future Value

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Future Value Definition, Future Value Formula for Simple Interest, Future Value

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