Question

Victor earns a gross annual income of $64,570 and is buying a home for $125,340. He is making a 15% down payment and financing the rest with a 20-year loan at 3.75% interest.

A. What is the mortgage amount he will borrow?
B. Can he afford this mortgage?
C. What will his monthly mortgage payment be?
D. What will his total payment for the house be?
E. What is the amount of interest he will pay?

Answer 1

Part (a): Mortgage amount to borrow
15% down payment will be made. Therefore, only 85% (100-15) will be borrowed.
That is,
Amount to borrow, P = $125,340*85/100 = $109,539

Part (b): Affordability
Gross annual income = $64,570
Less fixed expenses = (1-0.28)*64,570 = $46,490.40
If, on worse scenario, the loan is to be paid in four or so years, then net income can support that. Now, the loan is to be paid in 20 years and thus this is affordable.

Part (c): Monthly payments
Monthly payments, M = P[r(1+r)^n]/[(1+r)^n-1]

Where, r = 0.0375/12; n = 20*12 = 240 months

Substituting;
M = 109,539[0.0375/12(1+0.0375/12)^240]/[(1+0.0375/12)^240-1] = $640.44

Part (d): Total payment for the house
Total payment = Down payment + (Monthly payments*20*12) = (125,340 - 109,539) + (640.44*20*12) = 15801 + 153,705.60 = $169,506.60

Part (e): Total interest to be paid
Interest to be paid = Total payment - Cost of the home = 169,506.60 - 125,340 = $44,166.60