Question

Festus and Fran have decided to buy a house. The purchase price is $175,000. They have saved $25,000 for a down payment. The amount to be financed is $150,000. Consider the following two loan options for Festus and Fran:

I. Borrow $150,000 for 15 years (180 months) at 4% APR. What will the monthly payment be? How much total interest will Festus and Fran have to pay over the term of the loan?

II. Borrow $150,000 for 30 years (360 months) at 4.6% APR. What will the monthly payment be? How much total interest will Festus and Fran have to pay over the term of the loan?

If Festus and Fran intend to live in the house for 5-10 years, what advice do you have for Festus and Fran regarding their choice of loans? (You may want to consider looking up an amortization schedule for each before providing any advice.)

Answer 1

Mortgage Amount = $ 150000,

(I) Repayment Tenure = 15 years or (15 x 12) = 180 months, APR = 4 %

Applicable Monthly Interest Rate = 4 / 12 = 0.33 %

Let the monthly repayments be $ m

Therefore, 150000 = m x (1/0.0033) x [1-{1/(1.0033)^(180)}]

150000 = m x 135.5592

m = 150000 / 135.5592 = $ 1106.528

Total Repayment = 1106.528 x 180 = $ 199174.96

Interest Paid = Total Repayment - Borrowing = 199174.96 - 150000 = $ 49174.96

(II)

Repayment Tenure = 30 years or (15 x 30) = 360 months, APR = 4.6 %

Applicable Monthly Interest Rate = 4.6 / 12 = 0.3833 %

Let the monthly repayments be $ m

Therefore, 150000 = m x (1/0.003833) x [1-{1/(1.0038333)^(360)}]

150000 = m x 195.076

m = 150000 / 195.076 = $ 768.9307

Total Repayment = 768.9307 x 360 = $ 276815.0502

Interest Paid = Total Repayment - Borrowing = 276815.0502 - 150000 = $ 126815.0502

As is observable, the couple end up paying more interest for the longer tenure loan and that too at a higher rate even though the per month repayment for the same is lower than the alternative 180 month repayment option. Hence, the couple should opt for the 180 month loan.