Maths-
General
Easy

Question

Dubey borrows  Rs 1,00,000 from the State Bank of India at 11% p.a. compound interest. He repays Rs 41,000 at the end of the first year and  Rs47,700 at the end of the second year. Find the am not outstanding at the beginning of the third year.
 

Hint:

Find the interest every year, add it with the principal amount to get total amount and from that
subtract the repaid amount every year.

The correct answer is: 30000 Rupees


    Complete step by step solution:
    Money borrowed by Dubey at 11% compound interest, that is  = Rs 100000
    For first year,
    We know that compound interest = Total amount - principal amount that is, CI = A - P…(i)
    Here we have A equals P open parentheses 1 plus R over 100 close parentheses to the power of T…(ii)
    Here, we have T = 1 years, P = 100000 , R = 11% and A = ?
    On substituting the known values in (ii), we get A equals 100000 open parentheses 1 plus 11 over 100 close parentheses
    On substituting the known values in (i), we get C I equals 100000 open parentheses 1 plus 11 over 100 close parentheses to the power of blank space minus 100000
    not stretchy rightwards double arrow C I equals 100000 cross times 1.11 minus 100000
    not stretchy rightwards double arrow C I equals 11000 Rs
    Thus total amount after 1 year = 100000 + 11000 = 111000 Rupees.
    Money repaid = Rs 41000
    ∴ Balance = 111000 - 41000 = 70000 Rupees.
    For second year,
    Here, we have T = 1  years, P = 70000 , R = 11% and A = ?
    On substituting the known values in (ii), we get A equals 70000 open parentheses 1 plus 11 over 100 close parentheses
    On substituting the known values in (i), we get C I equals 70000 open parentheses 1 plus 11 over 100 close parentheses to the power of blank space minus 70000
    not stretchy rightwards double arrow C I equals 70000 cross times 1.11 minus 70000
    not stretchy rightwards double arrow C I equals 7700 Rs
    Thus total amount after 1 year = 70000 + 7700 = 77700 Rupees.
    Money paid at the end of second year by Dubey = Rs 47700
    ∴ Loan at the beginning of third year = 777000 - 47700 = Rs 30000

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