Question

A man borrows $Rs.10,000$ at $5\%$ per annum compound interest. He repays $35\%$ of the sum borrowed at the end of the first year and $42\%$ of the sum borrowed at the end of the second year. How much must he pay at the end of the third year in order to clear the debt ?

Answer 1

According to question,

$P=Rs.10,000$

$R=5\%$

$n=3$ years

Total amount on compound interest $\left(A\right)=P(1+\frac{R}{100}{)}^n$

For first year,

$A_1=10000(1+\frac{5}{100})$

$=10000\times \frac{105}{100}$

$=10500$

i.e., Amount at end of the first year, $=10500$

given that at the end of the first year he paid $35\%$ of the amount.

$35\%$ of the amount $=\frac{35}{100}\times 10000=Rs.3500$

Hence, for second year,

$P_2=Rs.10500-Rs.3500=Rs.7000$

$R=5\%$

$A_2=7000(1+\frac{5}{100})$

$\Rightarrow A_2=7000\left(\frac{105}{100}\right)$

$\Rightarrow A_2=Rs.7350$

Given that at the end of the second year he paid $42\%$ of the amount.

$42\%$ of the amount $=\frac{42}{100}\times 10000=Rs.4200$

Hence, for third year,

$P_3=Rs.7350-Rs.4200=Rs.3150$

$R=5\%$

$A_2=3150(1+\frac{5}{100})$

$=3150\times \frac{105}{100}$

$=Rs.3307.50$

Hence he should pay $Rs.3307.50$ at the end of the third year in order to clear his debt.