Janelle wishes to finance a car for $33,000. The bank's annual interest rate is 3.5%, and she can choose between durations of five or six years. Calculate the monthly payment and total amount paid for both duration options.
Use the formula, P=A(rn)(1+rn)nt(1+rn)nt−1
where A is the amount to finance, r is the annual interest rate, n is the number of times interest is applied per year, and t is the number of years. Show all of your steps.
(4 points)
For the 5-year duration:
P = A(rn)(1+rn)nt(1+rn)nt−1
P = 33000(0.035/12)(1+0.035/12)12(5)(1+0.035/12)12(5)−1
P = 33000(0.002917)(1+0.002917)60(1+0.002917)59
P = 33000(0.002917)(1.002917)^60(1.002917)^59
P = 33000(0.002917)(1.20004)(1.19773)
P = 33000(0.008752)(1.4361478934)
P = 33000(0.01257042316)
P = $414.19
The monthly payment for a 5-year duration is $414.19
Total amount paid = monthly payment x number of months
Total amount paid = $414.19 x 60 months
Total amount paid = $24,851.40
For the 6-year duration:
P = A(rn)(1+rn)nt(1+rn)nt−1
P = 33000(0.035/12)(1+0.035/12)12(6)(1+0.035/12)12(6)−1
P = 33000(0.002917)(1+0.002917)72(1+0.002917)71
P = 33000(0.002917)(1.002917)^72(1.002917)^71
P = 33000(0.002917)(1.24234)(1.23978)
P = 33000(0.009152073278)
P = $301.99
The monthly payment for a 6-year duration is $301.99
Total amount paid = monthly payment x number of months
Total amount paid = $301.99 x 72 months
Total amount paid = $21,767.28
Therefore, for the 5-year duration, the monthly payment is $414.19 and the total amount paid is $24,851.40.
For the 6-year duration, the monthly payment is $301.99 and the total amount paid is $21,767.28.