Question

Nandan borrowed Rs. $1,00,000$ at $20$% p.a. compounded half-yearly.
The maximum interest he can pay was approx $30,000$ at any time find for how much time he can borrow this amount ?

• A. $1\frac{2}{3}$ years
• B. $2\frac{1}{2}$ years
• C. $1\frac{1}{2}$ years
• D. $2$ years

Answer 1

Answer: (C)

$1\frac{1}{2}$ years

Max. interest will come where the time is maximum.

$A=P(1+\frac{r}{100}{)}^n$

$r=\frac{1}{2}\times 20\%=10\%$per interest period

$I=A-P$

$I=P(1+\frac{r}{100}{)}^n-P$

$⟹30000=100000\left[\right(1+\frac{10}{100}{)}^n-1]$

$⟹(1.1{)}^n=1.3⟹n=2.75\approx 3$

Time=$3\times 6=18$Months