Question

Find the rate per cent annum if $Rs.2,00,000$ amount to $Rs.2,31,525$ in $1\frac{1}{2}$ year interest being compounded half-yearly.

• A. $5$%
• B. $10$%
• C. $15$%
• D. $10.5$%

Answer 1

The correct option is B $10$%

$P=Rs.2,00,000$
Number of conversion period $\left(n\right)=1\frac{1}{2}\times 2=3$
$Amount(A{)}_3=Rs.2,31,525$
We know that
$A_3=P(1+i{)}^3$
$2,31,525=2,00,000(1+i{)}^3$
$2,31,525/2,00,000=(1+i{)}^3$
$1.157625=(1+i{)}^3$
$(1.05{)}^3=(1+i{)}^3$
$i=0.05$
$i$ is the Interest rate per conversion period (six months) $=0.05=5$% and Interest rate per annum $=5$% $\times 2=10$%.