Maths-
General
Easy

Question

A person invests  Rs10000 for two years at a certain rate of interest compounded annually. At the end of one year, the sum amounts to  Rs12000. Calculate (i). the rate of interest per annum (ii) the amount at the end of the second year

Hint:

Use simple interest to find the rate of interest and from that find total amount at the end of 2years.

The correct answer is: 14400 RUPEES


    Complete step by step solution:
    (i)
    We know the formula for total amount = A = P + SI…(i)
    where A is the total amount, P is the principal amount and SI is simple interest.
    (for 1st year, both simple interest and compound interest are the same)
    Here, we have A = 12000 Rs and P = 10000 Rs
    On substituting the known values in (i), we get SI = 12000 - 10000 = 2000
    So, we have SI = 2000 Rs
    We calculate simple interest by the formula,S I equals fraction numerator P T R over denominator 100 end fraction…(ii)
    where P is Principal amount, T is number of years and R is rate of interest
    Here, we have SI = 2000, P = 10000,T = 1 and R = ?
    On substituting the known values in (ii), we get 2000 equals fraction numerator 10000 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 2000 cross times 100 over denominator 10000 cross times 1 end fraction end cell row cell not stretchy rightwards double arrow R equals 200000 over 10000 equals 20 straight percent sign end cell end table
    Hence the rate of interest  R is 20%.
    (ii)
    We know that A equals P open parentheses 1 plus R over 100 close parentheses to the power of T…(iii)
    Here, we have T = 2 years, P = 10000 , R = 20%
    Amount at the end of second year will be,
    On substituting the known values in (iii), we get A equals 10000 open parentheses 1 plus 1 fifth close parentheses squared
    not stretchy rightwards double arrow A equals 10000 cross times open parentheses 6 over 5 close parentheses squared
    not stretchy rightwards double arrow A equals 14400 Rupees

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