Question

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Review the Monthly Principal & Interest Factor chart to answer the question: APR 30-Year Term 20-Year Term 15-Year Term 5.5 $5.68 $6.88 $8.17 6.0 $6.00 $7.16 $8.44 6.5 $6.32 $7.46 $8.71 7.0 $6.65 $7.75 $8.99 7.5 $6.99 $8.06 $9.27 The Renfroe household will be financing a principal balance of $392,650.00 for their property. They are trying to decide whether to take a 30-year or 20-year term mortgage. Based on their credit score, they qualify for an APR of 5.5%. Calculate the difference in total interest they would pay between the two terms. (4 points) Choose one of the following options. Only one is correct.
$121,012.83
$134,353.72
$154,547.04
$186,416.64​

Answer 1

The difference in total interest paid between a 30-year and a 20-year term mortgage at an APR of 5.5% is $154,372.40.

Step-by-step explanation:

To calculate the difference in total interest paid between a 30-year and 20-year term mortgage at an APR of 5.5%, we will first determine the monthly payment for each term using the given Monthly Principal & Interest Factor chart, and then calculate the total payment over the life of the loans.

For the 30-year term:
Monthly Payment = Principal x Factor
Monthly Payment = $392,650.00 x $5.68
Monthly Payment = $2,230.67
Total Payment over 30 years = Monthly Payment x 12 months x 30 years
Total Payment over 30 years = $2,230.67 x 12 x 30
Total Payment over 30 years = $802,641.20

For the 20-year term:
Monthly Payment = Principal x Factor
Monthly Payment = $392,650.00 x $6.88
Monthly Payment = $2,701.12
Total Payment over 20 years = Monthly Payment x 12 months x 20 years
Total Payment over 20 years = $2,701.12 x 12 x 20
Total Payment over 20 years = $648,268.80

Now, we subtract the initial loan amount to find the total interest paid for each term:
Total Interest for 30 years = Total Payment over 30 years - Principal
Total Interest for 30 years = $802,641.20 - $392,650.00
Total Interest for 30 years = $409,991.20

Total Interest for 20 years = Total Payment over 20 years - Principal
Total Interest for 20 years = $648,268.80 - $392,650.00
Total Interest for 20 years = $255,618.80

Finally, we find the difference in total interest between the two terms:
Difference in Total Interest = Total Interest for 30 years - Total Interest for 20 years
Difference in Total Interest = $409,991.20 - $255,618.80
Difference in Total Interest = $154,372.40