Now that you have understood the concept of compound interest and the formula for calculating the same, let’s move on to the shortcut to find compound interest:
If a sum of money subject to compound interest becomes x times in ‘a’ years and y times in ‘b’ years, then both of these sums can be related using the below shortcut formula:
Let’s derive this shortcut from the main formula.
Taking condition 1, the sum becomes x times in ‘a’ year and y times in ‘b’ year. Thus, using the compound interest formula,
(X) 1/a = (1 + r/100)………………………….(equation I)
In the same way, taking the next condition, the sum becomes y times in ‘b’ year, it becomes:
(Y) 1/b = (1 + r/100)………………………….(equation II)
On dividing equation I by II, we get:
Let’s now use this trick to solve an example.
Example 1: A sum of money subjected to compound interest becomes 4 times in 4 years. In how many years will it become 16 times itself?
Solution: By using (X) 1/a = (Y) 1/b
If an amount grows up to X rupees in T years and Y in (T+1) years subject to compound interest, then the percent of rate can be calculated as:
R% = (Y - X )/ X * 100
Example 2: If an amount of money grows up to ₹5,000 in 4 years and up to ₹7,000 in 7 years, find the rate percent.
R% = (7- 4) / 4 * 100