Question

Compute the compound interest on Rs. $4,000$ for $1^{1_{/2}}$ years at $10\%$ p.a. compounded half-yearly.

• A. $16,000$
• B. $630.50$
• C. $425.76$
• D. $1,640$

Answer 1

Answer: (B)

$630.50$

Principal P$=Rs.4,000$. Since the interest is compounded half-yearly the number of conversion periods in $1^{1_{/2}}$ years are $3$. Also the rate of interest per conversion period ($6$ months) is $10\%\times \frac{1}{2}=5\%$($0.05$ in decimal).
Thus the amount $A_n$(in Rs.) is given by
$A_n=P(1+i{)}^n$
$A_3=4,000(1+0.05{)}^3$
$=4,630.50$
The compound interest is therefore Rs. $(4,630.50-4,000)$
$=Rs.630.50$.