Question

At a certain rate of simple interest $Rs4050$ amounts to $Rs4576.50$ in $2$ years. At the same rate of simple interest, how much would $Rs1$ lakh amount to in $3$ years?

Answer 1

Given principal amount $P=Rs40000$
Total amount $A=Rs4576.50$
Time $T=2$ years
interest $=$ Total Amount $–$ Principal
$=Rs4576.50-Rs4050$
Thus, interest $=Rs526.50$

Let the rate of simple interest $=R\%$ per annum
Simple Interest formula, $I=\frac{PTR}{100}$
Then, R$=\frac{(I\times 100)}{(P\times T)}$
By substituting values of $P,T$ and $I$, we get
$=\frac{(526.50\times 100)}{(4050\times 2)}\%$ p.a.
On further calculation, we get,
$=\frac{(526.5\times 100)}{(405\times 2)}\%$ p.a.
$=\frac{5265}{810}\%$ p.a.
$\therefore R=6.5\%$ p.a.

Now, finding the total amount on principle of
$P=Rs1$ lakh with same interest $R=6.5\%$
$T=3$ years
Since, $I=\frac{(P\times R\times T)}{100}$
$=\frac{(100000\times 6.5\times 3)}{100}$
$=Rs1000\times 6.5\times 3$
$\therefore I=Rs19500$
Amount $=$ Principal $+$ Interest
$=100000+19500$
$=Rs119500$
Therefore, the total amount is $Rs119500$