Question : If a certain sum becomes two times in seven years at Compound Interest, then in how many years will it become eight times?
Option 1: 14 years
Option 2: 21 years
Option 3: 28 years
Option 4: 35 years
Correct Answer: 21 years
Solution :
The sum becomes 2 times in 7 years.
2P = P$(1+\frac{r}{100})^7$ using,
Amount = P[$(1+\frac{r}{100})^n$], where P is principal, $r$ is the rate of interest compounded annually for $n$ years.
⇒ $1+\frac{r}{100}$ = $2^{\frac{1}{7}}$.....................................(1)
Let the sum become 8 times in T years.
⇒ 8P = P$(1+\frac{r}{100})^T$.............................(2)
⇒ $1+\frac{r}{100}$ = $2^{\frac{3}{T}}$
From equations (1) and (2), we get:
⇒ $2^{\frac{1}{7}}$ = $2^{\frac{3}{T}}$
⇒ ${\frac{1}{7}}$ = ${\frac{3}{T}}$
⇒ $T$ = 21
Hence, the correct answer is 21 years.
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