Question

A sum of money doubles in 4 years at a certain rate of compound interest. In how many years will it become 8 times? 
 

• A. 8 years
• B. 10 years
• C. 12 years
• D. 16 years

Hint:

For compound interest problems with multiples, use the exponent rule: if amount becomes $k^m$ times in $n$ years, time for $k^{mn}$ times is $m \times n$ years.

Answer 1

The Correct Option is C

- Step 1: For compound interest, amount = $P(1 + \dfrac{R}{100})^n$. Given it doubles in 4 years: $2P = P(1 + \dfrac{R}{100})^4$, so $(1 + \dfrac{R}{100})^4 = 2$.
- Step 2: For 8 times, $8P = P(1 + \dfrac{R}{100})^n$, so $(1 + \dfrac{R}{100})^n = 8 = 2^3$.
- Step 3: Since $(1 + \dfrac{R}{100})^4 = 2$, we have $(1 + \dfrac{R}{100})^n = (2)^{n/4}$. Set $(2)^{n/4} = 2^3$.
- Step 4: Equate exponents: $\dfrac{n}{4} = 3$, so $n = 12$.
- Step 5: Verify: If $(1 + \dfrac{R}{100})^4 = 2$, then $(1 + \dfrac{R}{100})^{12} = (2)^3 = 8$.
- Step 6: Check options: Option (c) is 12 years, which matches.