Question

A sum of money becomes ₹ 8427 in 2 years and ₹ 8932.62 in 3 years, invested compounded annually. Find the rate of interest and the sum of money.

Answer 1

Step 1: Set up the equations using the compound interest formula.

The formula for compound interest is A = P(1 + r)^t, where A is the final amount, P is the principal sum, r is the annual interest rate and t is the time in years.

From the problem, we can create two equations:

For 2 years: 8427 = P(1 + r)²

For 3 years: 8932.62 = P(1 + r)³

Step 2: Calculate the rate of interest.

To find the rate of interest (r), divide the second equation by the first equation:

`8932.62/8427 = (P(1 + r)^3)/(P(1 + r)^2)`

1.06 = 1 + r

r = 1.06 – 1

r = 0.06

The rate of interest is 6%.

Step 3: Calculate the sum of money.

Substitute the value of r into the first equation to find the principal sum (P):

8427 = P(1 + 0.06)²

8427 = P(1.06)²

8427 = P(1.1236)

`P = 8427/1.1236`

P = 7500

The rate of interest is 6% and the sum of money is ₹ 7500.