Question

PMT equals StartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis Over left bracket 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt right bracket EndFraction
to determine the regular payment​ amount, rounded to the nearest dollar. The price of a small cabin is ​$45,000. The bank requires a​ 5% down payment. The buyer is offered two mortgage​ options: 20-year fixed at 8​% or​ 30-year fixed at 8​%, both with monthly payments. Calculate the amount of interest paid for each option. How much does the buyer save in interest with the​ 20-year option?
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Part 1
Find the monthly payment for the​ 20-year option.
​$
  
358
​(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 = 45,000 - 0.05(45,000) = 45,000 - 2,250 = $42,750.
Monthly rate = 0.08/12 = 0.0066666667.

20-year (240 months)
- Monthly payment ≈ $358 (given)
- Total paid = 358 × 240 = $85,920
- Interest paid = 85,920 − 42,750 = $43,170

30-year (360 months)
- Monthly payment = 42,750*(0.08/12) / [1 − (1+0.08/12)^(-360)] ≈ $314
- Total paid = 314 × 360 = $113,040
- Interest paid = 113,040 − 42,750 = $70,290

Interest saved with 20‑year vs 30‑year = 70,290 − 43,170 = $27,120.