A page from the saving bank account of Priyanka is given below:
Date Particulars Amount withdrawn (Rs) Amount deposited (Rs) Balance (Rs)
$03 / 04 / 2006$ B/F - - $4, 000.00$
$05 / 04 / 2006$ By cash - $2, 000.00$ $6, 000.00$
$18 / 04 / 2006$ By cheque - $6, 000.00$ $12, 000.00$
$25 / 05 / 2006$ To cheque $5, 000.00$ - $7, 000.00$
$30 / 05 / 2006$ By cash - $3, 000.00$ $10, 000.00$
$20 / 07 / 2006$ By self $4, 000.00$ - $6, 000.00$
$10 / 09 / 2006$ By cash - $2, 000.00$ $8, 000.00$
$19 / 09 / 2006$ To cheque $1, 000.00$ - $7, 000.00$
If the interest earned by Priyanka for the period of ending September, $2006$ is Rs. $175$ , find the rate of interest (in $%$ ).

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Solution

Principal up to the month of September, $P =$ Rs. $7, 000$
Total time from May to September, $T = 6$ months $= \frac{6}{12} = \frac{1}{2}$ years.
Let the rate of interest be $R %$ .
Then, Interest $= \frac{P \times R \times T}{100}$
$∴ 175 = \frac{7, 000 \times R \times 1}{100 \times 2}$
$\Rightarrow R = \frac{175 \times 100 \times 2}{7, 000}$
$\Rightarrow R = 5 %$

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June $10^{t h}$ $2006$	To Cheque	$4, 500$	-	$3, 280$
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Date	Particulars	Amount withdrawn (Rs)	Amount deposited (Rs)	Balance (Rs)
$03 / 04 / 2006$	B/F	-	-	$4, 000.00$
$05 / 04 / 2006$	By cash	-	$2, 000.00$	$6, 000.00$
$18 / 04 / 2006$	By cheque	-	$6, 000.00$	$12, 000.00$
$25 / 05 / 2006$	To cheque	$5, 000.00$	-	$7, 000.00$
$30 / 05 / 2006$	By cash	-	$3, 000.00$	$10, 000.00$
$20 / 07 / 2006$	By self	$4, 000.00$	-	$6, 000.00$
$10 / 09 / 2006$	By cash	-	$2, 000.00$	$8, 000.00$
$19 / 09 / 2006$	To cheque	$1, 000.00$	-	$7, 000.00$

Principal up to the month of September, P= Rs. 7,000Total time from May to September, T=6 months =612=12 years.Let the rate of interest be R%.Then, Interest =P×R×T100∴175=7,000×R×1100×2⇒R=175×100×27,000⇒R=5%