Question

A sum of money triples itself in 8 years at simple interest. In how many years will it become five times itself at the same rate?

• A. 12 years
• B. 20 years
• C. 16 years
• D. 24 years

Hint:

Use the formula \( SI = \frac{PRT}{100} \) and set interest as per the multiple increase in amount.

Answer 1

The Correct Option is C

The objective is to ascertain the time required for an initial sum of money to grow fivefold under a simple interest regime. This is contingent upon the fact that the same sum triples in 8 years.

1. Foundational Principles:

- Simple Interest (SI): Calculated solely on the principal amount over the duration of the investment.
- Calculation Rule: \( \text{SI} = \frac{P \times R \times T}{100} \)
- Total Value (A): Represented as \( A = P + \text{SI} \)
- A sum that triples implies the interest earned is equivalent to twice the principal, i.e., \( 2P \).

2. Provided Data:

- Investment grows to \( 3P \) in 8 years, indicating SI = \( 2P \).
- Applying the SI formula: \( 2P = \frac{P \times R \times 8}{100} \)

3. Interest Rate Determination:

\[2P = \frac{P \times R \times 8}{100} \Rightarrow 2 = \frac{R \times 8}{100} \Rightarrow R = \frac{200}{8} = 25\%\]

4. Time to Reach Fivefold Value:

For the sum to become five times its original value, the total interest required is \( 5P - P = 4P \).
Using the SI formula with the determined rate:\[4P = \frac{P \times 25 \times T}{100}\Rightarrow 4 = \frac{25T}{100}\Rightarrow T = \frac{4 \times 100}{25} = 16 \text{ years}\]

Conclusion:

The sum will achieve five times its initial value in 16 years.