Question

John borrowed Rs. 20,000 for 4 years under the following conditions: 10% simple interest for the first $2\frac{1}{2}$ years. 10% compound interest for the remaining one and a half years on the amount due after $2\frac{1}{2}$ years,the interest being compounded half-yearly.Find the total amount to be paid at the end of the four years.

Answer 1

For first $2\frac{1}{2}$ years : $P=Rs20000;R=10$
$\therefore Interest=Rs\frac{20000\times 10\times 5}{100\times 2}$ [As, interest is simple]
$=Rs.5000$
Amount due after $2\frac{1}{2}$ years $=Rs.20000+Rs.5000=Rs.25000$
For remaining $1\frac{1}{2}$ years $P=Rs.25000;n=\frac{3}{2}yearsandr=10$ per annum compounded half yearly.
$\therefore A=P{(1+\frac{r}{2\times 100})}^{n\times 2}=Rs.25000{(1+\frac{10}{2\times 100})}^{\frac{3}{2}\times 2}$

$=25000(1+\frac{1}{20}{)}^3$

$=25000(\frac{21}{20}{)}^3$

$=25000\times \frac{21}{20}\times \frac{21}{20}\times \frac{21}{20}$
$Rs.28940.63$
The total amount to be paid by John at the end of $4$ years $=$ Rs. $28940.63$