Question

The Williams are buying a house that costs $323,000 and can afford a 10% down payment. If the Williams want the lowest monthly payment, which loan option would you recommend?
a.
15 year fixed, 5% down at a fixed rate of 5.5%
b.
30 year FHA, 3.5% down at a fixed rate of 6.25%
c.
30 year fixed, 20% down at a fixed rate of 5.75%
d.
30 year fixed, 10% down at a fixed rate of 6%

Answer 1

Compute the monthly payment M = P * (r / (1 - (1+r)^-n)) where P = loan amount, r = monthly rate, n = number of months.

House = $323,000.
- a) 15-yr, 5% down → P = 323,000*(0.95)=306,850; r=0.055/12; n=180 → M ≈ $2,508
- b) 30-yr FHA, 3.5% down → P = 323,000*(0.965)=311,695; r=0.0625/12; n=360 → M ≈ $1,917
- c) 30-yr, 20% down → P = 323,000*(0.80)=258,400; r=0.0575/12; n=360 → M ≈ $1,507 (lowest, but requires 20% down — they only have 10%)
- d) 30-yr, 10% down → P = 323,000*(0.90)=290,700; r=0.06/12; n=360 → M ≈ $1,744

Because the Williams can afford only a 10% down payment, option c isn’t available. Among the feasible choices, option d (30-year fixed, 10% down at 6%) gives the lowest monthly payment. (Note: FHA mortgage insurance or other fees could change effective payments for option b.)