Question

The difference between the compound interest and the simple interest on $Rs.42000$ for two years is $Rs.105$ at the same rate of interest per annum. Find
$\left(i\right)$ the rate of interest
$\left(ii\right)$ the compound interest earned in second year.

Answer 1

P = Rs 42000 T=2 years

Let rate = r %

$S.I=\frac{PRT}{100}=\frac{42000\times r\times 2}{100}=840$ Rs

For C.I

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

$=42000(1+\frac{r}{100}{)}^2$

$=42000(1+\frac{r^2}{10000}+\frac{r}{50})$

$=42000+\frac{42r^2}{10}+840r$

C.I = A - P

$=42000+\frac{42r^2}{10}+840r-42000$

$=\frac{42r^2}{10}+840r$

Given $C.I-S.I=105$

$=\frac{42r^2}{10}+840r-840r=105$

$=\frac{42r^2}{10}=105$

$=42r^2=1050$

$=r^2=25$

r=5%

C.I at 2nd year = $42000(1+\frac{5}{100}{)}^2-42000$

$=42000(1.1025-1)=4305$ Rs