Question

A sum of money triples it self in 3 years at compound interest. In how many years will it becomes 9 times

• A. 9 years
• B. 6 years
• C. 12 years
• D. 5 years

Answer 1

The Correct Option is B

To determine the number of years required for the sum of money to become 9 times its original value at compound interest, we start by recognizing that the sum triples in 3 years. Let's denote the initial sum as \( P \). After 3 years at compound interest, the amount becomes \( 3P \). This gives us the equation for compound interest: \( A = P(1 + r)^n \), where \( A \) is the amount after time period \( n \), \( r \) is the annual interest rate, and \( P \) is the principal amount.

Since the amount triples in 3 years, we have:

\( 3P = P(1 + r)^3 \)

Dividing both sides by \( P \), we get:

\( 3 = (1 + r)^3 \)

We need to solve for \( (1 + r) \) but given the amount needs to become 9 times the principal, we set up another equation:

\( 9P = P(1 + r)^n \)

Dividing both sides by \( P \), we have:

\( 9 = (1 + r)^n \)

Using the earlier result \( 3 = (1 + r)^3 \), we can express \( (1 + r) \) as the cube root of 3:

\( (1 + r) = 3^{1/3} \)

Substitute in the equation \( 9 = (3^{1/3})^n \):

\( 9 = 3^{n/3} \)

We know that \( 9 \) is \( 3^2 \), so we have:

\( 3^2 = 3^{n/3} \)

Equating the exponents gives:

\( 2 = n/3 \)

Solving for \( n \), we multiply both sides by 3:

\( n = 6 \)

This confirms that the sum will become 9 times its original in 6 years. Hence, the correct answer is 6 years.