Question

In what time will $Rs.8,000$ amount to $Rs.8,820$ at $10$% p.a. interest compounded half-yearly?

• A. $2.5year$
• B. $4year$
• C. $3year$
• D. $1year$

Answer 1

The correct option is D $1year$

Interest rate per conversion period, $\frac{10}{2}=5$% $=0.05$
$Principal\left(P\right)=Rs.8,000$
$Amount\left(A_n\right)=Rs.8,820$
$A_n=P(I-i)n$
$8,820=8,000(1+0.05{)}^n$
$8,820/8,000=(1+0.05{)}^n$
$1.1025=(1.05{)}^n$
$\left(1.05\right)2=(1.05{)}^n$
$n=2$; Hence number of conversion period is $2$ and the required time $=\frac{n}{2}=\frac{2}{2}=1year$.