Question

The compound interest, calculated yearly on a certain sum of money for the second year is $Rs.1320$ and for the third year is $Rs.1452$. Calculate the rate of interest ad the original sum of money (in $Rs.$).

Answer 1

C.I. for the third year $=$ Rs. $1,452$.
C.I. for the second year $=$ Rs. $1,320$
$\therefore$ S.I on Rs. $1,320$ for one year $=$ Rs. $1,452-$ Rs. $1,320=$ Rs. $132$.
Rate of interest $=\frac{132\times 100}{1,320}=10\%$.
Let the original money be Rs. $P$.
Amount after $2$ year $-$ amount after one year $=C.I.$ for second year.
$P{(1+\frac{10}{100})}^2-P(1+\frac{10}{100})=1,320$
$P[{\left(\frac{110}{100}\right)}^2-\frac{110}{100}]=1,320$
$\Rightarrow P[{\left(\frac{11}{10}\right)}^2-\frac{11}{10}]=1,320\Rightarrow P(\frac{121}{100}-\frac{11}{10})=$ Rs. $1,320$
$\Rightarrow P\times \frac{11}{100}=Rs.1,320\Rightarrow P=\frac{1,320\times 100}{11}=$ Rs. $12,000$
$\therefore$ Rate of interest $=10\%$
and Original sum of money $=$ Rs. $12,000$