Question

he 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 loan amount and monthly payment (P&I) for each option using M = L * (r / (1 - (1+r)^-n)), where r = monthly rate and n = months.

Price = $323,000.

a) 15-yr, 5% down, 5.5%:
- Down = $16,150 → Loan L = $306,850
- r = 0.055/12 = 0.0045833, n = 180
- Monthly ≈ $2,507

b) 30-yr FHA, 3.5% down, 6.25%:
- Down = $11,305 → L = $311,695
- r = 0.0625/12 = 0.0052083, n = 360
- Monthly ≈ $1,917

c) 30-yr, 20% down, 5.75%:
- Down = $64,600 → L = $258,400
- r = 0.0575/12 = 0.0047917, n = 360
- Monthly ≈ $1,508

d) 30-yr, 10% down, 6%:
- Down = $32,300 → L = $290,700
- r = 0.06/12 = 0.005, n = 360
- Monthly ≈ $1,743

Lowest monthly payment is option c (30-year fixed, 20% down at 5.75%).