Question

Varun took out a loan of $ 25000 $ rupees from a bank, which charges $ 11\% $ interest compounded annually. He paid back $ 10000 $ rupees after $ 2 $ years. How much should he pay after one more year to settle the loan?

Answer 1

Hint: Here, first of all we will find the amount payable after two years considering the compound interest and then subtracting the amount paid in between and then taking the resultant value and again apply the amount formula payable to settle the loan amount.

Complete step-by-step answer:
Loan, $ P = Rs.{\text{ 25000}} $
Rate of interest, $ R = 11\% $
Term period, $ T = 2 $ years
Use formula $ A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T} $ and place the given data in it.
 $ A = 25000{\left( {1 + \dfrac{{11}}{{100}}} \right)^2} $
Take LCM and then simplify the above expression –
 $ A = 25000{\left( {\dfrac{{100 + 11}}{{100}}} \right)^2} $
Simplify the numerator adding the terms –
 $ A = 25000{\left( {\dfrac{{111}}{{100}}} \right)^2} $
Simplify the above expression removing the common factors from the numerator and the denominator.
 $ A = 30802.5 $ Rs.
Varun paid Rs. $ 1000 $
So, the remaining amount to be paid $ = 30802.5 - 10000 $ Rs.
Find the difference in the above expression –
Remaining amount to be paid $ = 20802.5 $ Rs.
Now, the amount to be paid after one year is
 $ A = 20802.5{\left( {1 + \dfrac{{11}}{{100}}} \right)^1} $
Take LCM and then simplify the above expression –
 $ A = 20802.5{\left( {\dfrac{{111}}{{100}}} \right)^1} $
Simplify the above expression –
 $ A = 23090.775 $ Rs.
The above expression can be re-written as –
 $ A = 23091 $ Rs.
Hence, Varun has to pay Rs. $ 23091 $
So, the correct answer is “ Rs. $ 23091 $ ”.

Note: Before simplification of the expression, first convert the percentage rate of interest in the form of the simple fraction or the decimals and then only start further simplification for the required resultant solutions. Always remember the difference between simple interest and compound interest and apply its concept accordingly and wisely. Compound interest is defined as the interest paid for the interest earned in the previous year along with the current year. Be good in multiples, factorization and do simplification carefully and wisely.