correct answer is: d) ₹420 ; ₹4420

Explanation

Here, we can use the simple interest formula to find the interest at the end of the first year.
Given:
Principal \left(P\right)\;=\;₹6000
Rate \left(R\right)\;=\;7\% p.a.
Time \left(T\right)\;=\;1 year _{[calculating the 1st year interest]}
We know,
Simple Interest (S.I.) =\large\frac{P\times R\times T}{100}
\therefore S.I. =₹\large\left(\frac{6000\times7\times1}{100}\right)
\rightarrow S.I. =₹420

So, the interest at the end of the first year is ₹420 .

Now, to find the principal at the beginning of the second year, we subtract the amount (₹2000) that Rajesh repaid from the principal and add the interest received at the end of the first year.
So, the principal at the beginning of the second year is =
₹\left(6000-2000\right)+420
\rightarrow₹6420-2000
\rightarrow₹4420
Ans: The interest at the end of the first year is ₹420 and the principal at the beginning of the second year is ₹4420.

Other ways to ask this same question are:
1. Find the interest accrued at the end of year one and the principal amount at the beginning of year two for a ₹6000 loan, after repaying ₹2000, with a 7% annual interest rate.
2. Calculate the interest for the initial year and the principal at the start of the following year for a ₹6000 loan, repaid by ₹2000, at an annual interest rate of 7%.
3. What is the interest due after the first year and the principal at the beginning of the second year for a loan of ₹6000, repaid by ₹2000, with an annual interest rate of 7%?