A sum of money placed at compound interest (compounding annually) doubles itself in 10 years. Find the time in which it will amount to 4 times itself.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 20 years
From the problem, the sum doubles in 10 years. Let the principal be P, and the final amount after 10 years is 2P. Using the compound interest formula:
A = P(1 + r)t
where:
A = final amount,
P = principal,
r = annual interest rate,
t = time in years.
⇒ 2P = P(1 + r)10
⇒ 2 = (1 + r)10
the final amount is 4P, so:
⇒ 4P = P(1 + r)t
⇒ 4 = (1 + r)t
⇒ 4 = (21/10)t
⇒ 4 = 2t/10
⇒ 22 = 2t/10
⇒ 2 = t/10
⇒ t = 20
The sum will amount to 4 times itself in 20 years.