Question

The price of a home is ​$150,000. The bank requires a​ 15% down payment. The buyer is offered two mortgage​ options: 15-year fixed at 9.5​% or​ 30-year fixed at 9.5​%, both with monthly payments. Calculate the amount of interest paid for each option. How much does the buyer save in interest with the​ 15-year option? Use the following formula to determine the regular payment amount.
PMT equals StartStartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis OverOver left bracket 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt right bracket EndEndFraction
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Part 1
Find the monthly payment for the​ 15-year option.
​$
  
1332
​(Round to the nearest dollar as​ needed.)
Part 2
Find the monthly payment for the​ 30-year option.
​$
  
enter your response here
​(Round to the nearest dollar as​ needed.)

Answer 1

Loan amount = 150,000 − 0.15(150,000) = 127,500.
Monthly rate i = 0.095/12 ≈ 0.0079166667.

Payment formula: PMT = P*(i) / (1 − (1+i)^−N), where N = months.

15‑year (N = 180):
PMT ≈ 127,500*(0.0079166667) / (1 − (1+0.0079166667)^−180) ≈ $1,332 (rounded).
Total paid = 1,331.90… × 180 ≈ $239,742 → Interest = 239,742 − 127,500 ≈ $112,242.

30‑year (N = 360):
PMT ≈ 127,500*(0.0079166667) / (1 − (1+0.0079166667)^−360) ≈ $1,073 (rounded).
Total paid = 1,072.77… × 360 ≈ $386,198 → Interest = 386,198 − 127,500 ≈ $258,698.

Savings with 15‑year vs 30‑year:
258,698 − 112,242 ≈ $146,456.

Answers:
- Monthly payment (15‑yr): $1,332
- Monthly payment (30‑yr): $1,073
- Interest paid (15‑yr): ≈ $112,242
- Interest paid (30‑yr): ≈ $258,698
- Interest saved by choosing 15‑yr: ≈ $146,456