Question

What sum of money will amount to ₹ 9240 in 2 years if the rates of interest for two successive years are 5% and 10%, respectively?

Answer 1

Given:

• Final amount (A) after 2 years = ₹ 9240
• Rate of interest for the first year = 5%
• Rate of interest for the second year = 10%
• We need to find the principal sum (P).

Step-wise calculation:

1. The amount after the first year, (A₁), using compound interest formula:

`A_1 = P(1 + 5/100)`

A₁ = P × 1.05

2. The amount after the second year, which is the final amount (A):

`A = A_1(1 + 10/100)`

A = P × 1.05 × 1.10

A = P × 1.155

3. Given, A = 9240,

So, P × 1.155 = 9240

`P = 9240/1.155`

P = 8000

The sum of money that will amount to ₹ 9240 in 2 years at rates of 5% and 10% for the two successive years is ₹ 8000.

Thus, the principal sum = ₹ 8000.