Question

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to determine the regular payment​ amount, rounded to the nearest dollar. Consider the following pair of mortgage loan options for a ​$145,000 mortgage. Which mortgage loan has the larger total cost​ (closing costs​ + the amount paid for points​ + total cost of​ interest)? By how​ much?
Mortgage​ A: 30​-year fixed at 9.25​% with closing costs of ​$1300 and 1 point.
Mortgage​ B: 30​-year fixed at 8.25​% with closing costs of ​$1300 and 4 points.
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Part 1
Choose the correct answer​ below, and fill in the answer box to complete your choice.
​(Do not round until the final answer. Then round to the nearest dollar as​ needed.)
A.
Mortgage A has a larger total cost than mortgage B by ​$
  
enter your response here.
B.
Mortgage B has a larger total cost than mortgage A by ​$
  
enter your response here.

Answer 1

A. Mortgage A has the larger total cost by $32,766.

Work (rounded only at the end)
- Mortgage A (9.25%): monthly rate = 0.0925/12 = 0.0077083333
- Monthly payment = [145000*(0.0077083333)] / [1 - (1+0.0077083333)^(-360)] ≈ $1,193
- Total paid = 1,192.74*360 ≈ $429,385 → Total interest ≈ 429,385 − 145,000 = $284,385
- Points = 1% of 145,000 = $1,450; closing = $1,300
- Total cost = 284,385 + 1,450 + 1,300 = $287,135

- Mortgage B (8.25%): monthly rate = 0.0825/12 = 0.006875
- Monthly payment ≈ $1,090
- Total paid ≈ 1,089.64*360 = $392,269 → Total interest ≈ 392,269 − 145,000 = $247,269
- Points = 4% of 145,000 = $5,800; closing = $1,300
- Total cost = 247,269 + 5,800 + 1,300 = $254,369

Difference: 287,135 − 254,369 = $32,766 (Mortgage A is larger).