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.
#SPJ1
