Question

Calculate the amount and compound interest on

(a) $Rs.10,800$ for $3$ years at $12\frac{1}{2}$% per annum compounded annually.

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

(c) $Rs.62,500$ for $1\frac{1}{2}$ years at $8$% per annum compounded half yearly.

(d) $Rs.8,000$ for $1$ year at $9$% per annum compounded half yearly.

(e) $Rs.10,000$ for $1$ year at $8$% per annum compounded half yearly.

Answer 1

a) Given:

Prinicipal ($P$) = $Rs.10800$, Rate($R$)= $12\frac{1}{2}\%=\frac{25}{2}\%$ paTime ($n$) = $3$ years
Since, $A=P{(1+\frac{r}{100})}^n$ $=10800{(1+\frac{12.5}{100})}^3$
$=10800\left(1.423\right)$
$=15377.34$
Thus, $A=Rs.15377.34$

$CI=A-P=15377-10800=Rs.4577.34$

b) Given:

Principal($P$) = $Rs.18000$

Rate ($r$) = $10\%$

Time(n) = $2\frac{1}{2}$years

Now, when time is in fraction, we use CI formula for the whole number of the mixed fraction and on the fraction part we use the formula of simple interest.

Thus, compound interest for $2$ years

$A=P{(1+\frac{r}{100})}^n=18000{(1+\frac{10}{100})}^2=18000\left(1.21\right)=21780$

Now, this will act as Prinipal for SI

$\Rightarrow SI=\frac{P\times R\times T}{100}=\frac{217800\times 10\times 1}{200}=10890$

$\therefore A=21780+10890=Rs.32670$ and
Therefore, $CI=A-P$
$=32670-18000$
$=Rs.14670$

c) Given:

Prinicpal($P$)=$Rs.62500$

Rate($r$)=$8\%$ pa $\Rightarrow \frac{8\%}{2}=4\%$compounded half yearly

Time($n$) = $1\frac{1}{2}$ years compounded yearly.

$\therefore n=\frac{3}{2}\times 2=3$ compounded half yearly

$A=P{(1+\frac{r}{200})}^n=62500{(1+\frac{4}{200})}^3=62500(1+\frac{1}{50}{)}^3=62500\times \frac{51}{50}\times \frac{51}{50}\times \frac{51}{50}=66325.5$
$A=Rs.66325.5$

$CI=A-P=Rs.66325.5-62500=Rs.3825.5$

d) Given:

Prinipal ($P$) = $Rs.8000$

Time($n$) = $1$ year compounded annually.

$\therefore n=1\times 2=2$ compounded half yearly

Rate($r$)=$\frac{9\%}{2}$ compounded half yearly

$A=P{(1+\frac{r}{200})}^n=8000{(1+\frac{9}{200})}^2=8000\left(1.092\right)=8736.2$

$A=Rs.8736.20$

$CI=A-P=Rs.736.20$

e) Given:

Principal($P$)=$Rs.10000$

Time($n$)=$1$ year compounded annually

$\therefore n=1\times 2=2$ compounded half yearly

Rate($r$) =$\frac{8\%}{2}$ compounded half yearly

$A=P{(1+\frac{r}{200})}^n=10000{(1+\frac{8}{200})}^2=10000\left(1.0816\right)=10816$

$A=Rs.10816$

Therefore, $CI=A-P=Rs.816$