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Maths-

General

Easy

Question

The compound interest, calculated yearly, on a certain sum of money for the second year is Rs1320 and for the third year is Rs1452. Calculate the rate of interest and the original sum of money.

hint Hint:

First find the interest and then rate of interest. From that find the principal amount.

The correct answer is: 12000 Rupees

Complete step by step solution:
Compound interest for third year = Rs 1452 Rupees
Compound interest for second year = Rs 1320 Rupees
So, difference = 1452 - 1320 = 132 Rupees.
Hence interest for third year = Rs 132 (simple interest and compound interest for 1 year is same)
We calculate simple interest by the formula, $S I equals fraction numerator P T R over denominator 100 end fraction$ …(i)
where P is Principal amount, T is number of years and R is rate of interest
Here, we have SI = 132,P = 1320 ,T = 1 and R = ?
On substituting the known values in (i), we get $132 equals fraction numerator 1320 cross times 1 cross times R over denominator 100 end fraction$
$table attributes columnspacing 1em end attributes row cell not stretchy rightwards double arrow R equals fraction numerator 132 cross times 100 over denominator 1320 cross times 1 end fraction end cell row cell not stretchy rightwards double arrow R equals 13200 over 1320 equals 10 straight percent sign end cell end table$
Let the principal amount = P
Amount after 1st year - Amount after 2nd year = Rs 1320
$not stretchy rightwards double arrow P open parentheses 1 plus 10 over 100 close parentheses squared minus P open parentheses 1 plus 10 over 100 close parentheses to the power of 1 equals 1320$
$not stretchy rightwards double arrow P open square brackets open parentheses 11 over 10 close parentheses squared minus open parentheses 11 over 10 close parentheses to the power of 1 close square brackets equals 1320$
$not stretchy rightwards double arrow P open square brackets open parentheses 121 over 100 close parentheses minus open parentheses 11 over 10 close parentheses close square brackets equals 1320$
$not stretchy rightwards double arrow P open square brackets open parentheses 11 over 100 close parentheses close square brackets equals 1320$
$not stretchy rightwards double arrow P equals 1200$ Rs
Hence rate of interest is 10% and original money is 12000 Rupees.

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