Question

A company borrows Rs 10000 on condition to repay it with compound interest at $5$% p.a . by annual instalments at Rs 1000 each. In how many years will the debt be paid off?

• A. 14.2
• B. 21.7
• C. 12.67
• D. None of these

Answer 1

The correct option is A 14.2

$\Rightarrow$ Company borrow Rs.10000 i.e. $pv=Rs.10000$ and $I=5\%=0.05$. $A$ is also given which is $Rs.1000$

$\Rightarrow$ Present value of annuity regular

$\Rightarrow$ $pv=A\times \left[\frac{(1+I{)}^n-1}{I\times (1+I{)}^n}\right]$

$\Rightarrow$ $10000=1000\times \left[\frac{(1+0.05{)}^n-1}{0.05\times (1+0.05{)}^n}\right]$

$\Rightarrow$ $(1.05{)}^n-0.5\times (0.5{)}^n=1$

$\Rightarrow$ $(1.05{)}^n=2$

Taking log both sides

$\Rightarrow$ $n=\frac{log2}{log1.05}$

$\therefore$ $n=14.2years$