Question

In: Finance

   How much more total interest will be paid on a 30-year fixed-rate mortgage for $100,000...

   How much more total interest will be paid on a 30-year fixed-rate mortgage for $100,000 at 9.25% compared with a 15-year mortgage at 8.5%?

Solutions

Expert Solution

Situation – 1 , 30-year fixed-rate mortgage for $100,000 at 9.25%

Yearly Payment = [ P x { r ( 1+r)n } ] / ( 1+r)n – 1

= [ $100,000 x { 0.0925 x ( 1.0925)30 } ] / ( 1.0925)30 – 1

= [ $100,000 x { 0.0925 x 14.21161 } ] / 13.21161

= [ $100,000 x 1.31457 ] / 13.21161

= $9,950.14

Total Interest Paid on Mortgage = Total Payment - Mortgage Loan Amount

= [$9,950.14 x 30 Years ] - $100,000

= $298,504.20 – 100,000

= $198,504.20

Situation – 2 , 15-year fixed-rate mortgage for $100,000 at 8.50%

Yearly Payment = [ P x { r ( 1+r)n } ] / ( 1+r)n – 1

= [ $100,000 x { 0.085 x ( 1.085)15 } ] / ( 1.085)15 – 1

= [ $100,000 x { 0.085 x 3.39974 } ] / 2.39974

= [ $100,000 x 0.28898 ] / 2.39974

= $12042.05

Total Interest Paid on Mortgage = Total Payment - Mortgage Loan Amount

= [$12042.05 x 15 Years ] - $100,000

= 180630.69 – 100,000

= $80,630.69

Here, $117,873.51 of more interest is paid in case of 30 Year Mortgage Loan as compared to 15 Year Mortgage Loan [ $198,504.20 - 80,630.69 = $117,873.51]


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