Question

A loan of ₹200000 at the interest rate of 6% p.a. compounded monthly is to be amortized by equal payments at the end of each month for 5 years. The monthly payment is:
[Given (1.005)^-60 = 0.74137220]

• A. ₹1,866.57
• B. ₹4,886.57
• C. ₹3,866.57
• D. ₹2,866.57

Answer 1

The Correct Option is C

The problem involves calculating the monthly payment needed to amortize a loan, which is compounded monthly over 5 years. Given:

• Principal Amount (\(P\)): ₹200,000
• Annual Interest Rate (\(R\)): 6%
• Number of Payments (\(N\)): 5 years, or 60 months
• Monthly Interest Rate (\(r\)): \( \frac{6}{12} \% = 0.5\% = 0.005 \)
• \((1 + r)^{-N} = (1.005)^{-60} = 0.74137220\)

The formula to calculate the monthly payment (\(M\)) for a compounded loan is:

\[M = \frac{P \times r}{1 - (1 + r)^{-N}}\]

Substituting the given values:

\[M = \frac{200000 \times 0.005}{1-0.74137220}\]

Simplifying further:

\[M = \frac{1000}{1 - 0.74137220} = \frac{1000}{0.25862780}\]

\[M \approx 3866.57\]

Thus, the monthly payment required is ₹3,866.57, making this the correct answer.