Have you always wanted to be able to do compound interest problems in your head? Perhaps not... but it's a very useful skill to have because it gives you a lightning fast benchmark to determine how good (or not so good) a potential investment is likely to be.
The rule says that to find the number of years required to double your money at a given interest rate, you just divide the interest rate into 72. For example, if you want to know how long it will take to double your money at eight percent interest, divide 8 into 72 and get 9 years.
Y = 72 / r and r = 72 / Y
where Y and r are the years and interest rate, respectively.
Compound Interest Curve
Suppose you invest $100 at a compound interest rate of 10%. The rule of 72 tells you that your money will double every seven years, approximately:
| Years | Balance | |
| Now | $100 | |
| 7 | $200 | (doubles every |
| 14 | $400 | seven years) |
| 21 | $800 |
If you graph these points, you start to see the familiar compound interest curve:
Practice using the Rule of 72
It's good to practice with the rule of 72 to get an intuitive feeling for the way compound interest works. So...
Why Stop at a Double?
There's nothing sacred about doubling your money. You can also get a simple estimate for other growth factors, as this calculator shows:
Why Does the Rule of 72 Work?
If you want to know more, see this explanation of why the rule of 72 works. (Brace yourself, because it's slightly geeked out.)
Double Your Money: The Rule of 72
The Rule of 72 is a quick and simple technique for estimating one of two things:
- The time it takes for a single amount of money to double with a known interest rate.
- The rate of interest you need to earn for an amount to double within a known time period.
The rule states that an investment or a cost will double when:
[Investment Rate per year as a percent] x [Number of Years] = 72.
When interest is compounded annually, a single amount will double in each of the following situations:
The Rule of 72 indicates than an investment earning 9% per year compounded annually will double in 8 years. The rule also means if you want your money to double in 4 years, you need to find an investment that earns 18% per year compounded annually.
You can confirm the rationality of the Rule of 72 as follows: Find factors on the FV of 1 Table that are close to 2.000. (The factor of 2.000 tells you that the present value of 1.000 had doubled to the future value of 2.000.) When you find a factor close to 2.000, look at the interest rate at the top of the column and look at the number of periods (n) in the far left column of the row containing the factor. Multiply that interest rate times the number of periods and you will get the product 72.
To use the Rule of 72 in order to determine the approximate length of time it will take for your money to double, simply divide 72 by the annual interest rate. For example, if the interest rate earned is 6%, it will take 12 years (72 divided by 6) for your money to double. If you want your money to double every 8 years, you will need to earn an interest rate of 9% (72 divided by 8).
Here's another way to demonstrate that the Rule of 72 works. Assume you make a single deposit of $1,000 to an account and wish for it to grow to a future value of $2,000 in nine years. What annual interest rate compounded annually will the account have to pay? The Rule of 72 indicates that the rate must be 8% (72 divided by 9 years). Let's verify the rate with the format we used with the FV Table:
To finish solving the equation, we search only the "n = 9" row of the FV of 1 Table for the FV factor that is closest to 2.000. The factor closest to 2.000 in the row where n = 9 is 1.999 and it is in the column where i = 8%. An investment at 8% per year compounded annually for 9 years will cause the investment to double (8 x 9 = 72).
Answer
Verified
Hint:- In 8 years money from Interest will be come equal to the principal
amount invested. So, money had been doubled in 8 years.
Let the initial amount of money invested will be Rs. x.
Then after 8 years money had become 2x.
Out of Rs. 2x, money from interest will be 2x – initial amount invested = 2x – x = x.
Let the rate of interest be r.
So, now we will use a simple interest formula.
According to Simple Interest (S.I) formula.
\[ \Rightarrow S.I. =
\dfrac{{PRT}}{{100}}\].
Where P is principal amount, R is rate of interest and T will be time period.
So, putting the values in the above formula. We will get,
\[ \Rightarrow x = \dfrac{{xr(8)}}{{100}}\]
On solving the above equation. We will get,
\[ \Rightarrow {\text{ }}r{\text{ }} = {\text{ }}\dfrac{{100}}{8}{\text{ }} = {\text{ }}12.5\]
Hence, the rate of interest to double a money in 8 years will be 12.5% per annum.
Note:- Whenever we came up with this type of problem where we are asked
to
find rate of interest then first, we will find the interest on principal amount by
subtracting principal amount from the money after 8 years and then we will
assume rate of interest to be r and then apply, Simple Interest formula and
find the required value of rate of interest.