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

First eliminate (c): it requires 20% down and they can only afford 10%.

Compute the monthly payment using the mortgage formula M = L * [r(1+r)^n]/[(1+r)^n − 1].

House price = $323,000.

a) 15-yr, 5% down, 5.5%
- Down = 0.05(323,000) = 16,150 → Loan L = 306,850
- r = 0.055/12 = 0.00458333, n = 180
- M ≈ $2,508/month

b) 30-yr FHA, 3.5% down, 6.25%
- Down = 0.035(323,000) = 11,305 → L = 311,695
- r = 0.0625/12 = 0.00520833, n = 360
- M ≈ $1,919/month
(plus any FHA mortgage insurance premium)

d) 30-yr, 10% down, 6.0%
- Down = 0.10(323,000) = 32,300 → L = 290,700
- r = 0.06/12 = 0.005, n = 360
- M ≈ $1,744/month

Therefore, for the lowest monthly payment choose (d) 30-year fixed, 10% down at 6.0%. (Note: FHA/PMI and total interest paid over the loan differ among options; this answer compares principal & interest monthly payments.)