A sum of Rs. 6,400 amounts to Rs. 8,100 in 8 years at a certain rate of interest, compounded annually. Find the amount received after 4 years when Rs. 2,240 are invested at same rate of compound interest (compounded annually).
Show answer & explanation
Correct answer: D
Explanation
Given:
P₁ = 6400
A₁ = 8100
Time = 8 years
P₂ = 2240
Time = 4 years
By the formula:
A = P(1 + r)ⁿ
8100 = 6400(1 + r)⁸
(1 + r)⁸ = 8100 / 6400
= 81 / 64
= (3/2)⁴
Hence
(1 + r)² = √(3/2)
Now
(1 + r)⁴ = √(81/64)
= 9/8
Now
A = 2240 × 9/8 = 2520
Amount after 4 years = ₹2520