The amount received on a certain sum at the same annual rate of interest after 3 years and 5 years on compound interest (compounding annually) is Rs. 10648 and Rs. 12884.08 respectively. What is that sum?
Show answer & explanation
Correct answer: D
Explanation
Given:
Amount after 3 years = ₹10648
Amount after 5 years = ₹12884.08
By the formula:
A = P(1 + r/100)ⁿ
After 3 years
P(1 + r/100)³ = 10648 …(1)
After 5 years
P(1 + r/100)⁵ = 12884.08 …(2)
(2) ÷ (1)
(1 + r/100)² = 12884.08 / 10648 = 1.21
1 + r/100 = √1.21 = 1.1
Now substitute in (1):
P(1.1)³ = 10648
P(1.331) = 10648
P = 10648 / 1.331
P = ₹8000