Question

Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs. You need a $200,000 loan Option 1 a 30-year loan at an APR of 10% Option 2 a 15-year loan at an APR of 9.5%. Find the monthly payment for each option. The monthly payment for option 1 is S The monthly payment for option 2 is S (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 S The total payment for option 2 is S (Use the answers from the previous step to find this answer Round to the nearest cent as needed) Compare the two options Which appears to be the better option? OA Option 2 will always be the better option B. Option 1 is the better option, but only if the borrower plans to stay in the same home for the entire term of the loan OC. Option 1 will always be the better option OD. Option 2 is the better option, but only if the borrower can afford the higher monthly payments over the entire term of the loan 0​

Answer 1

The monthly payment for option 1 is $1755.144 and option 2 is $2088.97, total amount for option 1 is $631851.84 and option 2 is $376014.6, and on comparing option 2 will be better option.

Given that for $200,000 loan Option 1 is a 30-year loan at an APR of 10% Option 2 is a 15-year loan at an APR of 9.5%.

A concept that implies that the future value of money will be lower than its present value due to several factors such as inflation is known as TVM(time of value money).

Monthly Payments

Option 1

Loan Amount = $200,000

Number of payments = 30×12 = 360

Monthly interest rate = 10%/12 = 0.008333333

Monthly payment = Loan amount (1+ monthly interest rate)ⁿ×monthly interest rate/[(1+monthly interest rate)ⁿ- 1]

Monthly payment=200,000×(1+0.008333333)³⁶⁰×(0.008333333)/[(1+0.008333333)³⁶⁰-1]

Monthly payment=33062.328/18.83739

Monthly payment=$1755.144

Option 2

Loan Amount = $200,000

Number of payments = 15 x 12=180

Monthly interest rate = 9.5%/12=0.00792

Monthly payment = 200,000(1+0.00792)¹⁸⁰(0.00792)/[(1+0.00792)¹⁸⁰-1]

Monthly payment=6553.096/3.137

Monthly payment=$2088.97

Total Payments

Option 1

As we've found out the monthly payments, we now need to multiply it by the number of months.

$1755.144×360 = $631851.84

Option 2

$2088.97×180 = $376014.6

Conclusion

Option 2 will always be the better option economically as it saves $255837.24 ($631851.84 - $376014.6) in total payments.

Hence, For $200,000 loan Option 1 a 30-year loan at an APR of 10% Option 2 a 15-year loan at an APR of 9.5% is the monthly payment for option 1 is $1755.144 and option 2 is $2088.97, total amount for option 1 is $631851.84 and option 2 is $376014.6, and on comparing option 2 will be the better option.

Learn more about monthly cost from here brainly.com/question/1476828.

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