Question

The difference between the compound interest and the simple interest on a sum of money for $1.5$years at $12\%$ per annum is Rs.$150$. Calculate the amount.

Answer 1

Let the amount be x,

then

simple interest for 1.5 years

$=\frac{PRT}{100}$ = $\frac{x\times 12\times 1.5}{100}$=$\frac{18x}{100}$ ---(1)

compound interest for 1 year

CI=x(1+r)=x(1+0.12)=1.12x

for neat 6 months

CI= 1.12x(1+0.06)=1.872x

net compound interest

CI=1.872x-x=0.1872x

now given CI-SI=150

0.1872x - 0.18x =150

0.0072x=150

x=$\frac{150}{0.0072}$=20,833.33 RS.

$\therefore$ The total amount is 20,833.33 RS.