Question

Calculating the interest on a semi-annually compounded basis, a sum of money lent at compound interest in a year amounts to Rs. 75,625 and in two years Rs. becomes 94,864. Find the rate of interest per annum.
1. 12 Percent
2. 6 Percent
3. 24 Percent
4. 18 Percent

Answer 1

Correct Answer - Option 3 : 24 Percent

Given:

The interest on a semi-annually compounded basis, a sum of money lent at compound interest in a year amounts to Rs. 75,625 and in two years becomes Rs. 94,864

Formula used:

Amount = P[1 + (R/200)]^2T; when Interest is compounded semi-annually

P = Principal

R = Rate of interest

T = Time period

Calculation:

In case 1:

75625 = P[1 + (R/200)]²     ----eq.(1)

In case 2:

94864 = P[1 + (R/200)]⁴     ----eq.(2)

Dividing eq.(2) by eq.(1)

94864/75625 = [1 + (R/200)]²

⇒ 308/275 = 1 + (R/200)

⇒ R/200 = 33/275

⇒ R = 24

∴ Rate of interest = 24%