Question

A sum invested at 8% p.a. amounts to Rs. 20,280 at the end of one year, when the interest is compounded half-yearly. what will be the compound interest (in Rs.) on the same sum for 2 years if the interest rate is the same as earlier and interest is compounded annually?
1. 3,260
2. 4,000
3. 2,750
4. 3,120

Answer 1

Correct Answer - Option 4 : 3,120

Given

The sum invested at 8% p.a. amounts to Rs. 20,280 at the end of one year, when the interest is compounded half-yearly.

Formula used

A = P(1 + R/100)^T

A = Amount

P = Principal

R = Rate

T = Time

Calculation

Let Principal be Rs.x

⇒ Time is compounded half yearly so, rate is 8/2 = 4%

⇒ x(1 + 4/100)² = 20280

⇒ x(104/100)² = 20280

⇒ x(26/25)² = 20280

⇒ x = (20280 × 25 × 25)/(26 × 26)

⇒ x = Rs.18750

⇒ Amount = 18750(1 + 8/100)²

⇒ A = (18750 × 27 × 27)/(25 × 25)

⇒ Amount = Rs.21870

⇒ CI = 21870 - 18750

∴ Compound interest for 2 years at the same rate is Rs.3120