Question

A certain sum amounts to Rs. 34400 in 6 years and to Rs. 24800 in 2 years at simple interest. The same sum will amount to Rs. x in 2 \(\frac{2}{3}\) years at the same rate, when the interest is compounded yearly. What is the value of x (nearest to a whole number)?
1. Rs. 25088
2. Rs. 26593
3. Rs. 26690
4. Rs. 27095

Answer 1

Correct Answer - Option 4 : Rs. 27095

Given:

A certain sum amounts to Rs. 34400 in 6 years and to Rs. 24800 in 2 years at simple interest

Calculation:

⇒ 4-year simple interest on a certain sum = 34400 - 24800 = 9600

⇒ 2-year simple interest on a certain sum = 9600/2 = 4800

⇒ The principle amount = 24800 - 4800 = 20,000

⇒ The rate of simple interest = (2400/20000) × 100 = 12%

⇒ Compounded amount = x

⇒ Amount compounded for 2 year  = (1 + 12/100)² × (20000) = 25088

⇒ Amount compounded for next 2/3 year = 25088 × (12/100) × (2/3) = 2007.04

⇒ x = 25088 + 2007.04 = 27095.04 ≈ 27095

∴ The required result will be 27095.