Question
Find the difference between the compound interest and the simple interest in $2$ years on $Rs.5,000$ at $8\%$ p.a. compounded annually.
✓
Answer
Here $P=$ Rs $5000 \cdot r=8 \% t=2$ years
For simple interest:
$ \text { S.I. }=\frac{ P \times r \times t }{100} $
$\text { S.I. }=\operatorname{Rs} \frac{5000 \times 8 \times 2}{100} $
$\text { S.I. }=\text { Rs } 800 $
For compound interest:
$ A=P\left(1+\frac{r}{100}\right)^n$
$ A=\text { Rs } 5000\left(1+\frac{8}{100}\right)^2$
$ A=\text { Rs } 5000 \times \frac{108}{100} \times \frac{108}{100} $
$ A=\text { Rs 5,832 } $
$ \text { C.I. }=A-P $
$\text { C.I. }=\text { Rs (5832 -5,000) }$
$\text { C.I. }=\text { Rs 832 }$
The difference in the compound interest and the simple interest
$=\operatorname{Rs}(832-800) $
$=\operatorname{Rs} 32 . $
For simple interest:
$ \text { S.I. }=\frac{ P \times r \times t }{100} $
$\text { S.I. }=\operatorname{Rs} \frac{5000 \times 8 \times 2}{100} $
$\text { S.I. }=\text { Rs } 800 $
For compound interest:
$ A=P\left(1+\frac{r}{100}\right)^n$
$ A=\text { Rs } 5000\left(1+\frac{8}{100}\right)^2$
$ A=\text { Rs } 5000 \times \frac{108}{100} \times \frac{108}{100} $
$ A=\text { Rs 5,832 } $
$ \text { C.I. }=A-P $
$\text { C.I. }=\text { Rs (5832 -5,000) }$
$\text { C.I. }=\text { Rs 832 }$
The difference in the compound interest and the simple interest
$=\operatorname{Rs}(832-800) $
$=\operatorname{Rs} 32 . $
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