Question

A borrowed Rs. 2,500 from B at 12% per annum compound interest. After 2 years, A gave Rs. 2, 936 and a watch to B to clear the account. Find the cost of the watch?

Answer 1

Hint: We start solving the problem by assigning a variable to the interest that was laid during the first year. We then apply the given interest rate to the borrowed amount using the fact that a% of b is defined as $ \dfrac{a}{100}\times b $ . We then add the obtained interest to the principal to get the total amount that must be paid after the first year. We then apply the rate of interest to the effective amount after the first year to get the interest during the second year. We then add this interest to the effective amount to get the final amount that needs to be paid after each year. We then subtract Rs. 2,936 from the obtained final amount to get the required cost of the watch.

Complete step by step answer:
According to the problem, we are given that ‘A’ borrowed Rs. 2,500 from ‘B’ at 12% per annum compound interest. We need to find the cost of the watch if ‘A’ gave Rs. 2, 936 and a watch to ‘B’ to clear the account after 2 years.
We know that in compound interest, the interest is paid on the principal amount after the first year which will be added to the principal amount. But the interest is paid on the amount which is the result obtained after adding the principal amount and interest in the first year after the second year.
Now, let us assume the interest paid during the first year be $ {{I}_{1}} $ .
So, we have $ {{I}_{1}}=12\%\text{ of }2500 $ . We know that a% of b is defined as $ \dfrac{a}{100}\times b $ .
 $ \Rightarrow {{I}_{1}}=\dfrac{12}{100}\times 2500 $ .
 $ \Rightarrow {{I}_{1}}=300 $ .
We need to add an interest of Rs. 300 to the principal amount Rs. 2,500.
So, the final amount that has to be paid after first year is $ Rs.\left( 2500+300 \right)=Rs.2800 $ .
Let us assume the interest paid during the second year be $ {{I}_{2}} $ .
So, we have $ {{I}_{2}}=12\%\text{ of }2800 $ . We know that a% of b is defined as $ \dfrac{a}{100}\times b $ .
 $ \Rightarrow {{I}_{2}}=\dfrac{12}{100}\times 2800 $ .
 $ \Rightarrow {{I}_{2}}=336 $ .
We need to add an interest of Rs. 336 to the principal amount Rs. 2,800.
So, the final amount that has to be paid after second year is $ Rs.\left( 2800+336 \right)=Rs.3136 $ .
According to the problem, we are given that ‘A’ gave Rs. 2,936 and a watch to ‘B’ to clear the account. So, the sum of the cost of the watch and Rs. 2,936 should be equal to Rs. 3136.
Let us assume the cost of the watch is ‘c’.
So, we get $ 2936+c=3136 $ .
 $ \Rightarrow c=200 $ .
 $ \, therefore, $ We have found the cost of the watch as Rs. 200.

Note:
Whenever we get this type of problem, we first need to check whether the given rate of interest is simple or compound. We should know that if the given rate of interest is simple, the interest that is added to the principal amount will be the same every year. We should confuse a% of b with $ a\times b $ instead of $ \dfrac{a}{100}\times b $ . Similarly, we can expect problems to find the cost of a watch if the amount is borrowed at 12% per annum simple interest.