Question

QUESTION 6

You have just obtained home financing from a bank. The principal amount is RM750,000 and the loan is to be repaid over a period of 20 years via equal end-of-the-month monthly installment payments. The bank charges an annual nominal rate of 6.6%. The calculations are based on the concept of amortization.

Required: i. Calculate the monthly installment payment amount.

ii. How much of the third monthly installment payment will go towards the repayment of principal?

iii. How much of the 75th monthly installment payment consists of the payment of interest? iv. If the monthly installment payment amount is constant, why does the amount of interest charged by the bank change as the loan repayment progresses?

Answer 1

i.

P = RM 750,000

Monthly interest rate (r) = Annual interest rate / 12 = 0.066 / 12 = 0.0055

Total number of monthly payments (n) = 20 * 12 = 240

Monthly installment payment amount for amortization is given by (M):

(P * r) / [1 - (1+r)^-n ] = (750,000 * 0.0055 ) / [1 - (1+0.0055)^-240 ] = 4125 / 0.7319 = RM 5,636.04

ii.

The formula to calculate principal amount remaining after i^th payout is given by:

P(i) = P [ 1 - ((1+r)^t - 1) / ((1+r)ⁿ - 1) ]

So Principal component for the 3rd payout = P(3) - P(2)

P(3) = 750000 [ 1 - ((1+0.0055)³ - 1) / ((1+0.0055)²⁴⁰ - 1) ] = 745,441.90

P(2) = 750000 [ 1 - ((1+0.0055)² - 1) / ((1+0.0055)²⁴⁰ - 1) ] =746,969.61

principal component of 3rd payout = 746,969.61 - 745,441.90 = 1,527.71

iii)

On similar lines calculate the principal component for 65th payout and subtract from monthly installment amount to get the payment of interest

P(65) = 750000 [ 1 - ((1+0.0055)⁶⁵ - 1) / ((1+0.0055)²⁴⁰ - 1) ] = 632,317.20

P (64) = 750000 [ 1 - ((1+0.0055)⁶⁴ - 1) / ((1+0.0055)²⁴⁰ - 1) ] = 634,463.69

principal component of 65th payout = 634,463.69 - 632,317.20 = 2,146.49

Interest component of 65th payout = monthly installment amount - principal component of 65th payout

= 5,636.04 - 2146.49 = RM 3489.55

Part iv:

Monthly installment payment amount is composed of principal component and the interest component. Although the monthly installment payment amount is constant, every month the outstanding principal amount is reduced by the principal component of the monthly installment payment amount. Since the outstanding principal amount reduces, the interest charged for this amount also reduces. Hence the interest amount charged by the bank changes (reduces) as the loan payment progresses and the corresponding principal amount paid increases.