Question

$Rs.800$ amounts to $Rs.920$ in $3$ years at a certain rate of interest. If the rate of interest by $3$%, what would the amount will become?

Answer 1

Recall, interest $\left(I\right)=amount\left(A\right)-principal\left(P\right)$. Hence,
$I=Rs.920-Rs.800=Rs.120$.
This interest is accrued in $T=3$ years, for the principal $Rs.800$. Using $I=\frac{PTR}{100}$ we get,
$R=\frac{100\times I}{P\times T}=\frac{100\times 120}{800\times 3}=5$.
Thus the original rate of interest is $5$%. After the increase of interest by $3$%, the new rate of interest, which we again denote by $R=5$% $+3$% $=8$%. The principal $P=Rs.800$ and the period $T=3$ years remain the same.
Therefore,
$I=\frac{PTR}{100}=\frac{800\times 3\times 8}{100}=192$.
Therefore, the new amount $=Rs.800+Rs.192=Rs.992$.