Question

Yadaiah for his family needs borrowed Rs. 5120 at $12\frac{1}{2}$% per annum compounded annually. How much amount he has to pay to clear the debt at the end of two year nine months? Also find total how much interest he has paid?

Answer 1

Reshma tried to solve this problem like this
She first converted the time in years. 2 year 9 months $=2\frac{9}{12}$ year = $2\frac{3}{4}$ years
She tried to substitute this in the known formula $A=5120{(1+\frac{25}{100})}^{2\frac{3}{4}}$
Now she was stuck. She asked her teacher, how would she find a power which is fractional?
The teacher gave her a hint. First find the amount for the whole part. Then use this as principal to get simple interest for $\frac{3}{4}$ year
So $A=P{(1+\frac{R}{100})}^n$
$A=5120{(1+\frac{25}{200})}^2$
$=5120{\left(\frac{225}{200}\right)}^2$
$=6480$
Interest for remaining 9 months $=6480\times \frac{25}{2}\times \frac{3}{4}\times \frac{1}{100}=Rs/607.50$
So Yadaiah has to pay at the end of $2$ year $9$ months
$=6480+607.50=Rs.7087.50$
So total compound interest $=7087.50-5120=Rs.1967.50$