Respuesta :
The monthly payment for loan A is greater than the monthly payments for loan B by $191.40, while the total interest for loan B is greater than the total interest for loan A by $1,522.20.
Comparison of Monthly Payments and Total Interest
These can be done using the formula for calculating the present value of an ordinary annuity as follows:
P = PV / (((1 - (1 / (1 + r))^n) / r)) …………………………………. (1)
Where;
1) For Installment Loan A, the monthly payments can be calculated as follows:
P = Monthly payment of Installment Loan A = ?
PV = Present value or the amount borrowed for a new car = $18,000
r = Monthly interest rate = 5.3% / 12 = 0.053 / 12 = 0.00441666666666667
n = Number of months = Number of years * 12 = 3 * 12 = 36
Substitute the values into equation (1) to find P, we have:
P = $18,000 / ((1 - (1 / (1 + 0.00441666666666667))^36) / 0.00441666666666667)
P = $18,000 / 33.2162172178177
P = $541.90
Therefore, the monthly payment of Installment Loan A is $541.90.
2) For installment Loan B, the monthly payments can be calculated as follows:
P = Monthly payment of Installment Loan B = ?
PV = Present value or the amount borrowed for a new car = $18,000
r = Monthly interest rate = 6.3% / 12 = 0.053 / 12 = 0.00525
n = Number of months = Number of years * 12 = 5 * 12 = 50
Substitute the values into equation (1) to find P, we have:
P = $18,000 / ((1 - (1 / (1 + 0.00525))^60) / 0.00525)
P = $18,000 / 51.3541976210894
P = $350.51
Therefore, the monthly payment of Installment Loan B is $350.51.
3) Total interest for Loan A can be calculated as follows:
Total interest for Loan A = (P of A * n of A) - PV of A
Total interest for Loan A = ($541.90 * 36) - $18,000
Total interest for Loan A = $19,508.40 - $18,000
Total interest for Loan A = $1,508.40
4) Total interest for Loan B can be calculated as follows:
Total interest for Loan B = (P of B * n of B) - PV of B
Total interest for Loan B = ($350.51 * 60) - $18,000
Total interest for Loan B = $21,030.60 - $18,000
Total interest for Loan B = $3,030.60
5) The comparison of the monthly payments for the two loans can be done as follows:
Difference between monthly payments for the two loans = P of A – P of B = $541.90 - $350.51 = $191.40
Therefore, the difference between monthly payments for the two loans calculated above implies that the monthly payment for loan A is greater than the monthly payments for loan B by $191.40.
6) The comparison of the total interest for the two loans can be done as follows:
Difference between total interest for the two loans = Total interest for Loan B - Total interest for Loan A = $3,030.60 - $1,508.40 = $1,522.20
Therefore, the difference between total interest for the two loans calculated above implies that total interest for loan B is greater than total interest for loan A by $1,522.20.
Learn more about the present value of an ordinary annuity here: https://brainly.com/question/11691655.
