Question

A man borrowed Rs \[25000\] from the bank at \[20\% \] compound interest. At the end of every year he paid Rs. \[8000\]. At the end of the third year, he wanted to clear the loan. How much should he pay to clear the loan?

Answer 1

Hint: Here we will find the simple interest and with the help of the simple interest we will find the amount to be paid every year. Hence we will pay the amount in third year which is the amount he has to pay to clear the loan.

Formula used: When \[P\] is the principal, \[R\] is the rate of interest and \[T\] is the time, then simple interest is \[\dfrac{{PRT}}{{100}}\]

Complete step-by-step answer:
It is given that a man borrowed Rs\[25000\] from the bank at \[20\% \] compound interest. At the end of every year he paid Rs. \[8000\].
Compound interest is the simple interest for every year. For compound interest, the interest will be added to the principal for next year. For the next year the interest will be calculated principal and interest together.
For one year, compound interest and simple interest are the same.
We know that, when \[P\] is the principal, \[R\] is the rate of interest and \[T\] is the time, then simple interest is \[\dfrac{{PRT}}{{100}}\].
For first year, let us substitute \[P = 25000,R = 20\% ,T = 1\] in the simple interest formula, we get,
Simple interest \[ = \dfrac{{25000 \times 20 \times 1}}{{100}}\]
Let us simplify the above equation then we get,
The simple interest \[ = Rs.5000\]
Hence the amount\[ = Rs.25000 + 5000 = Rs.30000\]
Now, it is clear that he paid Rs \[8000\] at the end of every year.
For second year,
Principal would be \[P = Rs.30000 - 8000 = Rs.22000\]
Now let us substitute \[P = 22000,R = 20\% ,T = 1\]in simple interest formula then we have,
Simple interest \[ = \dfrac{{22000 \times 20 \times 1}}{{100}}\]
By simplifying we get,
The simple interest \[ = Rs.4400\]
Hence the amount\[ = Rs.22000 + 4400 = Rs.26400\]
Now, he paid Rs.\[8000\] at the end of every year.
For third year,
Principal would be \[P = Rs.26400 - 8000 = Rs.18400\]
Now let us substitute \[P = 18400,R = 20\% ,T = 1\]in simple interest formula then we have,
Simple interest \[ = \dfrac{{18400 \times 20 \times 1}}{{100}}\]
On simplifying the above equation we get,
The simple interest\[ = Rs.3680\]
So, amount \[ = Rs.18400 + 3680 = Rs.22080\]
Hence, he should pay \[Rs.22080\] to clear his loan.

Note: Since, the person paid Rs. \[8000\] at the end of every year, so we will consider it as the interest for a single year. That means we will calculate simple interest instead of compound interest.