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:

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.

    Related Questions to study

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.