Question
Calculate the amount and the compound interest for the following, when cornpounded half-yearly:
$Rs.25,000$ for $1 \frac{1}{2}$ years at $12 \%$
$Rs.25,000$ for $1 \frac{1}{2}$ years at $12 \%$
✓
Answer
$P=\operatorname{Rs} 25,000 ; t=1 \frac{1}{2}$ years $; r=12 \%$ p.a. $=6 \%$ half-early.
$A=P\left(1+\frac{r}{100}\right)^n $
$A=\operatorname{Rs} 25000\left(1+\frac{6}{100}\right)^2\left(1+\frac{12}{100}\right)^{\frac{1}{2}} $
$ =\text { Rs } 25,000 \times 1.06 \times 1.06 \times\left(1+\frac{1}{2} \times \frac{12}{100}\right)$
$=\text { Rs } 25,000 \times 1.06 \times 1.06 \times 1.06 $
$=\text { Rs29,775.40 } \\ \text { C.I. }=A-P $
$=\text { Rs }(29,775.40-25,000) $
$ =\text { Rs } 4,775.40$
Hence, Amount $= Rs.29,775.40$ and C.I. $=Rs.4,775.40$
$A=P\left(1+\frac{r}{100}\right)^n $
$A=\operatorname{Rs} 25000\left(1+\frac{6}{100}\right)^2\left(1+\frac{12}{100}\right)^{\frac{1}{2}} $
$ =\text { Rs } 25,000 \times 1.06 \times 1.06 \times\left(1+\frac{1}{2} \times \frac{12}{100}\right)$
$=\text { Rs } 25,000 \times 1.06 \times 1.06 \times 1.06 $
$=\text { Rs29,775.40 } \\ \text { C.I. }=A-P $
$=\text { Rs }(29,775.40-25,000) $
$ =\text { Rs } 4,775.40$
Hence, Amount $= Rs.29,775.40$ and C.I. $=Rs.4,775.40$
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