Question : A sum of money placed at compound interest doubles itself in 5 years. In how many years would it amount to eight times itself at the same rate of interest?
Option 1: 10 years
Option 2: 15 years
Option 3: 7 years
Option 4: 20 years
Correct Answer: 15 years
Solution :
By applying the formula: Amount = P[$(1+\frac{r}{100})^n$] where P is principal, $r$ is the rate of interest compounded annually for $n$ years.
Let the sum be $x$, then:
Amount = $x(1+\frac{r}{100})^5 = 2x$
⇒ $(1+\frac{r}{100})^5 = \frac{2x}{x}=2$
⇒ $(1+\frac{r}{100})=2^\frac{1}{5}$
Now, the sum becomes 8 times after $n$ years, then:
$x(1+\frac{r}{100})^n = 8x$
⇒ $(1+\frac{r}{100})^n = \frac{8x}{x}=8=2^3$
⇒ $2^\frac{n}{5} = 2^3$
Thus, $n$ = 5 × 3 = 15 years
Hence, the correct answer is 15 years.
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