Arithmetic

Simple & Compound Interest

Easy

An amount doubles itself at compound interest in 5 years. How many years will it take to make the amount 16 times itself ?

✅ Correct Option: 4

Let the initial amount be $P$ and rate of interest be $r\%$

Given that amount doubles in 5 years:

$P(1 + \frac{r}{100})^5 = 2P$

$(1 + \frac{r}{100})^5 = 2$

Now, let's say it takes $x$ years to make the amount 16 times:

$P(1 + \frac{r}{100})^x = 16P$

$(1 + \frac{r}{100})^x = 16$

We know that $16 = 2^4$

$[(1 + \frac{r}{100})^5]^{\frac{x}{5}} = 2^4$

$2^{\frac{x}{5}} = 2^4$

Therefore:

$\frac{x}{5} = 4$

$x = 20$

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