Question

An amount becomes three times of itself on compound interest (compounding annually) in 4 years. In how many years at the same rate on compound interest (compounding annually) it will become 9 times of itself?

• A. 10
• B. 12
• C. 8
• D. 16

Answer 1

Answer:

C. 8

Solution:

Assume:

Principal = P

Rate = R%

Given:

Time = 4 years

Formula used:

Amount = P(1 + R/100)T

Where, P = Principal, T = Time, and R = rate of interest

Calculation:

Amount = P(1 + R/100)T

In 4 years:

3P = P(1 + R/100)⁴ 

3 = (1 + R/100)⁴ 

Now;

Amount will be 9 times:

Amount = P(1 + R/100)T

9P = P(1 + R/100)^T

9 = (1 + R/100)^T

3² = (1 + R/100)^T

[(1 + R/100)4]² = (1 + R/100)^T

(1 + R/100)⁸ = (1 + R/100)^T

T = 8 years

Hence, option (C) is the correct answer.