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Maths-

General

Easy

Question

On what sum of money will the difference between the compound interest and simple interest for 2years be equal to Rs 25 if the rate of interest charged for both is 5% p.a.

hint Hint:

Use the formula of compound interest and simple interest to get the principal amount.

The correct answer is: Rs 10000

Complete step by step solution:
Let the principal amount = P
It is given that the rate of interest R = 5% and number of years T = 2 years.
So, compound interest for 2 years = $P open parentheses 1 plus 5 over 100 close parentheses squared minus P$
Simple interest for 2 years = $S I equals fraction numerator P cross times 2 cross times 5 over denominator 100 end fraction equals P over 10$
It is given that compound interest - simple interest = 25 Rupees
That is, $P open parentheses 1 plus 5 over 100 close parentheses squared minus P minus P over 10 equals 25$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow fraction numerator 441 P over denominator 400 end fraction minus fraction numerator 11 P over denominator 10 end fraction equals 25 end cell row cell not stretchy rightwards double arrow fraction numerator 441 P minus 440 P over denominator 400 end fraction equals 25 end cell end table$
$not stretchy rightwards double arrow P equals 10000$ Rupees.
Hence the principal amount = Rs 10000

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