A sum becomes 4 times its original value in 6 years under compound interest. In how many years will it become 16 times of the original amount?
Show answer & explanation
Correct answer: A
Explanation
Amount in 6 years = 4 times the Principal
A = P(1 + r)ᵗ
In 6 years:
P(1 + r)⁶ = 4P
(1 + r)⁶ = 4
Let us assume that in t years, the amount becomes 16P.
P(1 + r)ᵗ = 16P
(1 + r)ᵗ = 16
16 = 4²
(1 + r)⁶ = 4
(1 + r)¹² = 16
t = 12 years