Step-by-Step Solution

Topic: Time Value of Money & Amortization

PRELIMINARY CALCULATIONS

1. Monthly Interest Rate (i):

i = 6.75% / 12 = 0.5625% = 0.005625

2. Total Number of Installments (n):

n = 10 years × 12 months = 120 months

(I) CALCULATE MONTHLY INSTALMENT (EMI)

Using the EMI formula:

Substitute the values:

EMI = 40,00,000 × [ 0.005625 / (1 – 0.510120) ]

EMI = 40,00,000 × [ 0.005625 / 0.48988 ]

EMI = 40,00,000 × 0.0114824

(II) OUTSTANDING PRINCIPAL (Beginning of 61st Month)

We calculate the balance after 60 payments have been made.
Formula: Balance = P(1+i)^n’ – EMI [ ((1+i)^n’ – 1) / i ]
Where n’ = 60 (months passed).

Step 1: P(1+i)⁶⁰ = 40,00,000 × 1.400115 = 56,00,460

Step 2: EMI Component = 45,929.61 × [ (1.400115 – 1) / 0.005625 ]

    = 45,929.61 × [ 0.400115 / 0.005625 ]

    = 45,929.61 × 71.13155 ≈ 32,67,040

Step 3: Balance = 56,00,460 – 32,67,040

(III) BREAKDOWN OF 61st INSTALMENT

(a) Interest Amount (I₆₁):

Interest is calculated on the outstanding principal at the start of the month.

I₆₁ = P₆₀ × i = 23,33,420 × 0.005625

(b) Principal Amount Paid:

Principal Component = EMI – Interest Component

Principal = 45,929.61 – 13,125.49