Question

Calculate the amount and compound interest on:-

$1)Rs.10,8000$ for $3$ years at $12\frac{1}{2}\%$ per annum compounded annually.

$2)Rs.18,000$ for $2\frac{1}{2}$ years at $10\%$ per annum compounded annually.

$3)Rs.65,500$ for $1\frac{1}{2}$ years at $8\%$ per annum compounded half yearly.

Answer 1

$1).$

$P=Rs108000$

$R=12\frac{1}{2}\%$

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

$T=3$ years

So,

$\begin{array}{cc}A& =P{\left(1+\frac{R}{100}\right)}^t\\ & =108000{\left(1+\frac{25}{200}\right)}^3\\ & =108000{\left(1+\frac{1}{8}\right)}^3\\ & =108000{\left(\frac{9}{8}\right)}^3\\ & =108000\times \frac{9}{8}\times \frac{9}{8}\times \frac{9}{8}\\ & =Rs.153773.4\end{array}$

And,

Interest $=$ Amount $-$ Principal

$=Rs.153773.4-Rs.108000$

$=Rs.45,773.4$

$2).$

$P=Rs.18000$

$R=10\%$

$T=2\frac{1}{2}$

$=\frac{5}{2}$ years

So,

$\begin{array}{cc}A& =P{\left(1+\frac{R}{100}\right)}^t\\ & =18000{\left(1+\frac{10}{100}\right)}^2\\ & =18000\times \frac{11}{10}\times \frac{11}{10}\\ & =Rs.21780\end{array}$

The interest after two years will be $Rs.21780-Rs.18000=Rs.3780$

Now, interest for the next half year,

$I^{\prime }=21780\times \frac{10}{100}\times \frac{1}{2}$

$=Rs.1089$

So, total interest will be $Rs.1089+Rs.3780=Rs.4869$

And, total amount will be $Rs.21,780+Rs.1089=Rs.22,869$

$3).$

$P=Rs.65,500$

$R=4\%$ but as the interest is compounded half yearly $R^{\prime }=2\%.$

$T=1\frac{1}{2}$ years but as the interest is compounded half yearly $T^{\prime }=1.5$ years.

So,

$\begin{array}{cc}A& =65500{\left(1+\frac{4}{100}\right)}^3\\ & =65500{\left(\frac{26}{25}\right)}^3\\ & =65500\times \frac{26}{25}\times \frac{26}{25}\times \frac{26}{25}\\ & =Rs.73678.5\end{array}$

And,

Interest $=$ Amount $-$ Principal

$=Rs.73678.5-Rs.65500$

$=Rs.8178.5$