Question

Rekha borrowed Rs.40,000 for 3 years at 10% per annum compound interest. Calculate the interest earned in the second year.

Answer 1

Hint: First we find the interest after the first year by applying the formula of interest. Take the interest obtained from the first year and add it to the principal amount to get the principal amount for the second year. Apply the formula of interest to find the interest in the second year.
* If $P$ is the principal amount, $R$ is the rate of interest compounded annually; $A$ is the amount or interest received after $T$ years then \[A = PRT\]

Complete step by step answer:
We are given that Rekha borrowed $Rs.40,000$ for a time period of $3$ years at a rate of interest $10\%$ per annum compounded annually.
So, after each year we get a new value of interest after adding the interest from the previous year to the principal amount.

For the first-year:
We find the interest earned for the first year.
Substitute the value of \[P = 40,000\], \[R = 10\% \] and \[T = 1\] in the formula of interest.
\[ \Rightarrow A = PRT\]
\[ \Rightarrow A = 40000 \times \dfrac{{10}}{{100}} \times 1\]
Cancel the same factors from numerator and denominator in RHS of the equation.
\[ \Rightarrow A = 4000\]
The Principal amount for the second year is the sum of interest from the first-year plus the principal amount.
\[ \Rightarrow P + A = 40,000 + 4,000\]
\[ \Rightarrow P + A = 44,000\]

For the second year:
We find the interest earned in the second year.
Let P’ be the principal amount and A’ be the interest earned in the second year.
Substitute the value of \[P' = 44,000\], \[R = 10\% \] and \[T = 1\] in the formula of interest.
\[ \Rightarrow A' = P'RT\]
\[ \Rightarrow A' = 44000 \times \dfrac{{10}}{{100}} \times 1\]
Cancel the same factors from numerator and denominator in RHS of the equation.
\[ \Rightarrow A' = 4400\]

Therefore, the interest earned in the second year is Rs. 4400.

Note:
Students might get confused with the word compounded annually and apply the formula for compound interest in this question to find the interest. Keep in mind the interest we calculate is for each year and we use the concept of compound interest by adding the interest of first-year to give us the increased value of the principal amount for the second year. We use the formula of compound interest when we have to calculate the interest at the end of the total time period.