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# In how many years will ruppes 4000 amount to rupee 4630.50 at 5%p.a.compounded annually

**Given: **Principal $P=₹\ 4000$, Amount with interest $A=₹\ 4630.50$, rate $r=5$ %.

**To do: **To find the number of years $t=?$

**Solution: **

As known, $A=P( 1+\frac{r}{100})^t$

$\Rightarrow 4630.50=4000( 1+\frac{5}{100})^t$

$\Rightarrow 4630.50=4000( 1+\frac{1}{20})^t$

$\Rightarrow \frac{463050}{2}=4000( \frac{20+1}{20})^t$

$\Rightarrow \frac{9261}{8000}=( \frac{21}{20})^t$

$\Rightarrow \frac{21\times21\times21}{20\times20\times20}=( \frac{21}{20})^t$

$\Rightarrow ( \frac{21}{20}|)^3=( \frac{21}{20})^t$

$\Rightarrow n=3$

Thus, in $3$ years the amount will be $₹\ 4630.50$.

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