Question

A sum amounts to Rs. 29282 after 2 years when compounded half yearly at rate of interest 20%. Find the amount when same sum compounded annually at same rate of interest for same time.
1. Rs. 28800
2. Rs. 25282
3. Rs. 22000
4. Rs. 24200

Answer 1

Correct Answer - Option 1 : Rs. 28800

Given:

Amount after 2 years = Rs. 29282 (compounded half yearly)

Rate of interest = 10%

Formula:

Amount when compounded annually = P(1 + R/100)ⁿ

Amount when compounded half yearly = P(1 + R/200)²ⁿ

Here, P = Principal, R = rate of interest and N = time period

Calculation:

Amount = P(1 + R/200)2n

29282 = P(1 + 20/200)⁴

⇒ 29282 = P × 1.1⁴

⇒ P = Rs. 20000

Sum invested is Rs. 20000.

Amount when compounded annually = 20000(1 + 20/100)² = Rs. 28800

∴ Amount will be Rs. 28800 when compounded annually