Question

Calculate the amount and compound interest on

i) $Rs.15000$ for $2$ years at $10\%$ per annum compounded annually.

ii) $Rs.156250$ for $1\frac{1}{2}$ years at $8\%$ per annum compounded half yearly.

iii) $Rs.100000$ for $9$ months at $4\%$ per annum compounded quarterly.

Answer 1

$\left(i\right)$

Given:

$P=Rs.15000$

$n=2$ years

$r=10\%$ per annum

Now the total amount on Compound interest,

$A=P{(1+\frac{r}{100})}^n$

$=15000{(1+\frac{10}{100})}^2$

$=15000{(1+\frac{1}{10})}^2$

$=15000{\left(\frac{11}{10}\right)}^2$

$=15000\times \frac{11}{10}\times \frac{11}{10}$

$=150\times 121$

$=Rs.18150$

$\therefore A==Rs.18150$

$CI=A-P$

$=Rs.18150-Rs.15000$

$\therefore C.I=Rs3150$

$\left(ii\right)$

Given:

$P=Rs.156250$

$n=1\frac{1}{2}=1.5$ years

$r=8\%$ per annum

Now the total amount on Compound interest,

$A=P{(1+\frac{r}{m\times 100})}^{n\times m}$

$=156250{(1+\frac{8}{2\times 100})}^{1.5\times 2}$

$=156250{(1+\frac{1}{25})}^3$

$=156250{\left(\frac{26}{25}\right)}^3$

$=156250\times \frac{26}{25}\times \frac{26}{25}$

$=10\times 26\times 26\times 26$

$=Rs.175760$

$\therefore A=Rs.175760$

$CI=A-P$

$=Rs.175760-Rs.156250$

$=Rs.19510$

$\therefore C.I=Rs.19510$

$\left(iii\right)$

Given:

$P=Rs.100000$

$n=9$ months $=\frac{9}{12}=0.75$ years

$r=4\%$

Now the total amount on Compound interest,

$A=P{(1+\frac{r}{m\times 100})}^{n\times m}$

$=100000{(1+\frac{4}{4\times 100})}^{0.75\times 4}$

$=100000{(1+\frac{1}{100})}^3$

$=100000{\left(\frac{101}{100}\right)}^3$

$=100000\times \frac{101}{100}\times \frac{101}{100}\times \frac{101}{100}$

$=\frac{101\times 101\times 101}{10}$

$\therefore A=Rs103030.1\approx Rs103030$

$CI=A-P$

$=Rs.3030$

$\therefore C.I=Rs.3030$