Question

A man borrows Rs. $20,000$ at $10$% S.I. for $2\frac{1}{2}$ years. He immediately invests the entire amount for $2\frac{1}{2}$ years at $10$% compounded annually. What is his gain at the end of the stipulated time, when he repays his loan?

Answer 1

For the amount the man borrows,
$N=2\frac{1}{2}=\frac{5}{2}years$
$R=10$ %
$P=Rs20,000$
The interest he will have to pay $S.I.=\frac{PNR}{100}=\frac{20,000\times \frac{5}{2}\times 10}{100}=Rs5000$
And for the amount the man invests,
We first calculate the C.I. for first $2$ years and then the S.I. next $\frac{1}{2}$ year.
For ,
$N=2years$
$R=10$ %
$=>P=Rs20,000$
And on interest being compounded we have,
$Amount=P{(1+\frac{R}{100})}^N=20,000\times {(1+\frac{10}{100})}^2=20,000\times {1.1}^2=Rs24,200$
So, $C.I$ for first $2$ years $=A-P=Rs24,200=Rs20,000=Rs4,200$
This, $Rs24,200$ is the principal for the next $\frac{1}{2}$ year.
So, $S.I.=\frac{PNR}{100}=\frac{24,200\times \frac{1}{2}\times 10}{100}=Rs1,210$
Thus, total interest earned $=Rs4,200+Rs1,210=Rs5,410$
And Amount $=Rs8,000+Rs3,373.50=Rs11,373.50$
Hence, his gain $C.I$ interest earned from investing $-S.I.$ paid for borrowing it $=5,410-5,000=Rs410$