Assume the car can be purchased for 0% down for 60 months (in lieu of rebate).
A car with a sticker price of $42,650 with factory and dealer rebates of $5,100
a-Find the monthly payment if financed for 60 months at 0% APR. (Round your answer to the nearest cent.
b-Find the monthly payment if financed at 2.5% add-on interest for 60 months. (Round your answer to the nearest cent.
c-Use the APR approximation formula to find the APR for part (b).
(d) State whether the 0% APR or the 2.5% add-on rate should be preferred.
0% APR or 2.5% add-on rate
a. (42,650-5100)/60 = %625.83/mo.
b. P = (Po*r*t)/(1-(1+r)^-t)
Po = 42,650-5100 = 37550
r = (2.5%/12)/100% = 0.00208
t = 60 Months.
Plug the above values into the given Eq and get:
P = $39,984.81
39984.81/60mo = $666.41/mo. = Monthly payments.
c. I = (39984.81-37550)/5yrs = $486.96/
yr.
APR = (486.96/37550)*100% = 1.30%
To find the monthly payment for each financing option, we need to calculate the loan amount first.
a) For 0% down financing, the loan amount is the sticker price minus any rebates:
Loan amount = Sticker price - Rebates = $42,650 - $5,100 = $37,550
Now, to calculate the monthly payment for 60 months at 0% APR, we use the formula for a fixed-rate loan:
Monthly payment = Loan amount / Number of months = $37,550 / 60 = $625.83 (rounded to the nearest cent)
b) For financing at a 2.5% add-on interest rate, the loan amount is the sticker price minus any rebates:
Loan amount = Sticker price - Rebates = $42,650 - $5,100 = $37,550
To calculate the monthly payment for 60 months at a 2.5% add-on interest rate, we need to convert the add-on interest rate to an effective annual interest rate. The add-on rate is multiplied by the number of years (0.025 * 5), and then divided by the number of monthly payments (60) to get the monthly interest rate:
Monthly interest rate = (Add-on rate * Number of years) / Number of monthly payments = (0.025 * 5) / 60 = 0.002083
Now, we can use the formula for a fixed-rate loan with interest added on:
Monthly payment = (Loan amount + (Loan amount * Monthly interest rate)) / Number of months = ($37,550 + ($37,550 * 0.002083)) / 60 = $642.55 (rounded to the nearest cent)
c) To calculate the APR using the approximation formula, we need to solve the equation for APR in terms of the loan amount, monthly payment, and number of months:
APR = [(Monthly payment * Number of months) / Loan amount - 1] * 12 * 100
Using the values from part (b):
APR = [(642.55 * 60) / 37550 - 1] * 12 * 100 = 3.17%
d) To determine which financing option is preferred, we compare the 0% APR and the 2.5% add-on rate. In general, a lower interest rate is preferred because it results in lower monthly payments and less overall interest paid over the loan term. Therefore, the 0% APR is the better choice in this case.