Quiz: Week 5 Checkpoint This Question: 1 pt 9 of 12 (3 Compare the monthly payme
ID: 2817984 • Letter: Q
Question
Quiz: Week 5 Checkpoint This Question: 1 pt 9 of 12 (3 Compare the monthly payments and total loan costs for the You need a $170,000 loan. same closing costs Option 1: a 30-year loan at an APR of 9% Option 2: a 15-year loan at an APR of 8.5%. Find the monthly payment for each option. The monthly payment for option 1 is The monthly payment for option 2 is (Do not round until the final answer. Then round to the nearest cent as needed) Find the total amount paid for each option The total payment for option 1 is The total payment for option 2 is (Use the answers from the previous step to find this answer Round to the neareat cent as needed) Compare the two options Which appears to be the better option? but O B. Option 1 will always be the better option. O C. Option 2 will always be the better option O D. Option 1 is the better option, but only if the borrower plans to stay in the same home for the entire term of the loanExplanation / Answer
Option 1:
30-year loan at an APR of 9%:
Amount borrowed = $170,000
Annual Interest Rate = 9%
Monthly Interest Rate = 0.75%
Period = 30 years or 360 months
Monthly Payment * PVIFA(0.75%, 360) = $170,000
Monthly Payment * (1 - (1/1.0075)^360) / 0.0075 = $170,000
Monthly Payment * 124.28187 = $170,000
Monthly Payment = $1,367.86
Total Payment = Monthly Payment * Number of Payments
Total Payment = $1,367.86 * 360
Total Payment = $492,429.60
Option 2:
15-year loan at an APR of 8.50%:
Amount borrowed = $170,000
Annual Interest Rate = 8.50%
Monthly Interest Rate = 0.7083%
Period = 15 years or 180 months
Monthly Payment * PVIFA(0.7083%, 180) = $170,000
Monthly Payment * (1 - (1/1.007083)^180) / 0.007083 = $170,000
Monthly Payment * 101.55211 = $170,000
Monthly Payment = $1,674.02
Total Payment = Monthly Payment * Number of Payments
Total Payment = $1,674.02 * 180
Total Payment = $301,323.60
Option 2 is the better option, but only if the borrower can afford the higher payments over the entire term of the loan.
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