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.
For a duration of five years:
P = 33000(0.035/12)(1+(0.035/12))^(12*5)/(1+(0.035/12))^(12*5 - 1)
P = 33000(0.00291666667)(1.00291666667)^60/(1.00291666667)^59
P = 33000(0.09647)/0.09251
P = 3176.17
Monthly payment for a five-year duration: $3176.17
Total amount paid for a five-year duration: $3176.17 * 60 = $190,570.20
For a duration of six years:
P = 33000(0.035/12)(1+(0.035/12))^(12*6)/(1+(0.035/12))^(12*6 - 1)
P = 33000(0.00291666667)(1.00291666667)^72/(1.00291666667)^71
P = 33000(0.00291666667)(1.22433)/1.21941
P = 3895.54
Monthly payment for a six-year duration: $3895.54
Total amount paid for a six-year duration: $3895.54 * 72 = $280,276.88
In conclusion, Janelle's monthly payment would be $3176.17 for a five-year duration, and $3895.54 for a six-year duration. The total amount paid would be $190,570.20 for a five-year duration, and $280,276.88 for a six-year duration.