Question

Thomas took out a loan of 15000 rupees from a bank which charges $12\% $ interest, compounded annually. After 2 years, he paid back 10000 rupees. To settle the loan, how much should he pay at the end of 3 years?

Answer 1

Hint:
We can find the amount after the 2 years using the formula for compound interest. Then we can subtract the amount paid after two year to get the remaining amount. Then we can calculate the interest of the remaining amount for next year by taking the remaining amount as the principal amount. This amount of interest will give us the amount he must pay to settle the loan.

Complete step by step solution:
It is given that the loan amount is Rs. 15000 and interest that the bank charges is $12\% $
 $ \Rightarrow P = 15000$
 $ \Rightarrow R = 12 \% $
Now we can calculate the amount with compound interest at the end of 2 years. We know that equation for the amount of compound interest is given as $A = P{\left( {1 + \dfrac{R}{{100}}} \right)^N}$ where P is the principal amount, N is the number of years and R is the rate of interest.
On substituting the values of P, R and N, we get,
 $ \Rightarrow A = 15000{\left( {1 + \dfrac{{12}}{{100}}} \right)^2}$
On simplification we get,
 $ \Rightarrow A = 15000{\left( {1 + 0.12} \right)^2}$
On adding terms in bracket, we get,
 $ \Rightarrow A = 15000{\left( {1.12} \right)^2}$
On squaring the terms, we get,
 $ \Rightarrow A = 15000 \times 1.2544$
On multiplication we get,
 $ \Rightarrow $ A=18816
Thus, the amount to be paid after 2 years will be Rs. 18816.
But he paid only Rs. 10000.
Then the remaining loan to be paid is,
 $ \Rightarrow P' = 18816 - 10000$
On subtraction we get,
 $ \Rightarrow P' = 8816$ .
Now we can find the interest amount after one year using equation of compound interest $A = P{\left( {1 + \dfrac{R}{{100}}} \right)^N}$
Here, P changes to Rs. 8816 and N is 1 year.
 $ \Rightarrow A' = 8816{\left( {1 + \dfrac{{12}}{{100}}} \right)^1}$
On simplification we get,
 $ \Rightarrow A' = 8816\left( {1 + 0.12} \right)$
On adding terms in bracket, we get,
 $ \Rightarrow A' = 8816 \times 1.12$
On multiplication we get,
 $ \Rightarrow A' = 9873.92$

So, the amount of money Thomas must pay to settle the loan at the end of three years is Rs. 9873.92

Note:
The difference between simple interest and compound interest is that in simple interest, the interest is calculated on the principal year every year. In compound interest, the interest is calculated for the total amount after adding the interest of the previous year. The amount after compound interest will become the simple interest when the number of years is 1. So, in this question we can find the amount after interest using the equation of simple interest. We must note that the equation of compound interest will give the total amount after adding the interest and the equation for simple interest will give only the interest.