Question

A man borrows Rs.12500 from a bank at 20% compound interest. At the end of every year, he pays Rs.2000 as part repayment. How much does he still owe to the bank after such installments?
A.Rs.15600
B.Rs.12864
C.Rs.12000
D.Rs.14320

Answer 1

Hint: In this question, calculate compound interest for every year and subtract the installments that the man pays every year from compound interest for 3 years.
Compound interest is the addition of interest to the principal sum of loan given by the formula,
\[A = P{\left( {1 + \dfrac{r}{n}} \right)^{\left( n \right)\left( t \right)}}\]Where A is the amount, P is the principle, R is the rate of interest, T is the time of the investment, n=number of times interest applied per time period and CI is the compound interest.

Complete step-by-step answer:
Given the amount Rs.12500 borrowed by the man from the bank at 20% compound interest
The principle for the first year will be \[P = Rs.12500\]
Hence the amount he has to pay after one year,
 \[
  A = 12500{\left( {1 + \dfrac{{20}}{{100}}} \right)^1} \\
   = 12500\left( {\dfrac{{120}}{{100}}} \right) \\
   = 12500 \times \dfrac{6}{5} \\
   = Rs15000 \\
 \]
The amount he has to pay after one year is Rs.15000.
The actual amount the man pay after one year is Rs.2000
So the principle for the second year will be given as:
\[15000 - 2000 = Rs.13000\]
Now the amount for the second year will be,
\[
  A = 13000{\left( {1 + \dfrac{{20}}{{100}}} \right)^1} \\
   = 13000\left( {\dfrac{{120}}{{100}}} \right) \\
   = 13000 \times \dfrac{6}{5} \\
   = Rs15600 \\
 \]
Hence the amount he has to pay after the second year is Rs.15600,
The actual amount the man pay for the second year is Rs.2000
So the principle for the third year will be =15600-2000=Rs.13600
Now the amount for the third year will be,
\[
  A = 13600{\left( {1 + \dfrac{{20}}{{100}}} \right)^1} \\
   = 13600\left( {\dfrac{{120}}{{100}}} \right) \\
   = 13600 \times \dfrac{6}{5} \\
   = Rs16320 \\
 \]
Hence the amount he has to pay after the third year is Rs.16320,
The actual amount the man pay for the third year is Rs.2000
Therefore after 3 years, the amount he owes is:
\[16320 - 2000 = Rs.14320\]
So, the correct answer is “Option D”.

Note: Students can also solve this question by finding compound interest for 3 years together and subtracting it by the repayment that is calculated for each year compounded.