Question

The difference between compound interest and simple interest on an amount of ₹15,000 for 2 years is ₹96. What is the rate of interest per annum? [3 Marks]

Answer 1

Given that, principal, $P=₹15000$ and time period, $n=2$ years .
Let the rate of interest per annum be $r$. [0.5 Mark]
Simple interest in 2 years
$S.I=\frac{15000\times r\times 2}{100}$
$\Rightarrow S.I=300r$ [0.5 Mark]

Compound interest $C.I=A-P=15000(1+\frac{r}{100}{)}^2-15000$, here, $A$ is the amount. [0.5 Mark]


In compound interest, ​​​​​​the interest is calculated on the amount of the previous year. Therefore it is known as interest compounded or Compound Interest (C.I.)
We know that after the first year, C.I > S.I

Given that $C.I-S.I=96$ [0.5 Mark]

(Since C.I > S.I)
$\Rightarrow 15000(1+\frac{r}{100}{)}^2-15000-300r=96$
$\Rightarrow 15000(1+\frac{r}{100}{)}^2-300r=15096$
$\Rightarrow 15000(1+\frac{r^2}{10000}+\frac{2r}{100})-300r=15096$
$\Rightarrow 15000+\frac{15r^2}{10}+300r-300r=15096$
$\Rightarrow \frac{15r^2}{10}=96$
$\Rightarrow 15r^2=960$
$\Rightarrow r^2=64$
$\Rightarrow r=\pm 8$
$\because$ Rate of interest cannot be negative, so $r=8\%$ [1 Mark]