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# Calculate the amount and compound interest on Rs. 10,800 for 3 years at $ 12 \frac{1}{2} \% $ per annum compounded annually.

**Given:**

Principal \( (P)=10,800 \)

Time \( =3 \) years

Rate \( (\mathrm{R})=12 \frac{1}{2} \) per annum compounded annually.

$=\frac{25}{2} \%$

**To do:**

We have to calculate the amount and compound interest.**Solution:**

We know that,

Amount \( (\mathrm{A})=\mathrm{P}\left(1+\frac{R}{100}\right)^{n} \)

Therefore,

Amount$=10,800(1+\frac{\frac{25}{2}}{100})^{3}$

$ =10800(1+\frac{1}{8})^3$

$=10800\times(\frac{8+1}{8})^3$

$=10800\times\frac{9\times9\times9}{8\times8\times8}$

$=\frac{1350\times729}{64}$

$=\frac{984150}{64}$

$=Rs.\ 15377.34$

Amount$=$Principal$+$Interest

Therefore,

Interest$=Rs.\ (15377.34-10800)$

$=Rs.\ 4577.34$

**Amount and compound interest after 3 years is Rs. 15377.34 and Rs. 4577.34 respectively. **

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