Question : If a certain sum becomes 3 times in 6 years at compound interest, then in how many years, it will become 81 times?
Option 1: 81 years
Option 2: 162 years
Option 3: 27 years
Option 4: 24 years
Correct Answer: 24 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 = $x(1+\frac{r}{100})^6 = 3x$
⇒ $(1+\frac{r}{100})^6 = \frac{3x}{x}=3$
⇒ $(1+\frac{r}{100}) =3^\frac{1}{6}$
Now, the sum becomes 81 times after $n$ years, then:
$x(1+\frac{r}{100})^n = 81x$
⇒ $(1+\frac{r}{100})^n = \frac{81x}{x}=81=3^4$
⇒ $3^\frac{n}{6} = 3^4$
Thus, $n$ = 6 × 4 = 24 years
Hence, the correct answer is 24 years.
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