Michelle is debating between two different mortgages for $184,000. She found a 20-year fixed rate loan at 7.05% and 15-year fixed rate loan at the same rate. How much more interest will she pay for the 20-year loan versus the 15-year loan?

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  $45,081

Step-by-step explanation:

The amortization formula can be used to find the monthly payment.

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

For the 20-year loan with r=0.0705 and P=184,000, the monthly payment is ...

  A = $1432.08

The total amount repaid will be ...

  12×20×1432.08 = 343,699.20

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For the 15-year loan with the same parameters, the monthly payment is ...

  A = 1658.99

and the total amount repaid is ...

  12×15×1658.99 = 298,618.20

The difference in these repayment amounts is the difference in interest charges:

  343,699.20 -298,618.20 = 45,081

The 20-year loan will cost $45,081 more than the 15-year loan.

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