Assume the car can be purchased for 0% down for 60 months (in lieu of rebate).
A car with a sticker price of $42,500 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). (Round your answer to one decimal place.)
(d) State whether the 0% APR or the 2.5% add-on rate should be preferred.
0% APR
2.5% add-on rate
a) since 0% interest, the monthly payment would simply be
42500/60 = $708.33
b) I believe in the US , add-on-interest is done this way:
amount to be financed = 42500-5100 = 37400
interest = 37400(.025)(5) = 4675.00
total of loan = 37400 + 4675 = 42075.00
monthly payment = 42075/60 = 701.25
c) not familiar with the approximation formula used in the US (I am in Canada)
d) which method gave us the lower payment?
The method used in b) gives an effective rate of much higher than 2.5%, and would be often misunderstood by the consumer.
Done in the proper compound interest method :
i = .025/12 = .00208333...
n = 60
37400 = paym( 1 - 1.00208333..^-60)/.002083333..
payment = 663.75
To find the monthly payment, we'll need to use the loan amount, interest rate, and loan term.
(a) For the 0% APR financing, the loan amount will be the sticker price minus the rebates: $42,500 - $5,100 = $37,400.
Using an online loan calculator or the PMT function in a spreadsheet program, we can find the monthly payment.
PMT(rate, nper, PV)
Where:
rate = 0% APR (which is 0), but we'll enter it as 0.00 in the calculation
nper = 60 (months)
PV = -$37,400 (note the negative sign indicating payment)
Using the PMT function, we get a monthly payment of $623.33.
(b) For the 2.5% add-on interest financing, the loan amount will again be $37,400.
To calculate the monthly payment using the add-on interest method, we add the interest to the loan amount and divide by the number of months.
Total amount financed = loan amount + (loan amount * interest rate)
Total amount financed = $37,400 + ($37,400 * 0.025)
Total amount financed = $37,400 + $935
Total amount financed = $38,335
Monthly payment = Total amount financed / number of months
Monthly payment = $38,335 / 60
Monthly payment = $639.92
(c) To find the APR approximation for the 2.5% add-on interest rate, we can use the formula:
APR = (add-on rate / (1 - add-on rate)) * 12 * 100
APR = (2.5% / (1 - 2.5%)) * 12 * 100
APR = (0.025 / (1 - 0.025)) * 12 * 100
APR = 0.025 / 0.975 * 12 * 100
APR = 30.769%
The APR approximation for the 2.5% add-on interest rate is approximately 30.8%.
(d) Comparing the 0% APR and the 2.5% add-on rate, the 0% APR should be preferred. This is because with 0% APR, there is no interest charged on the loan, resulting in a lower monthly payment compared to the 2.5% add-on rate.
(a) To find the monthly payment if financed for 60 months at 0% APR, we can simply divide the sticker price by the number of months. Since there is 0% APR, there won't be any interest on the loan. Here's how you can calculate it:
Monthly Payment = Sticker Price / Number of Months
Monthly Payment = $42,500 / 60
Using a calculator, you can find that the monthly payment works out to be $708.33 (rounded to the nearest cent).
(b) To find the monthly payment if financed at 2.5% add-on interest for 60 months, we use a slightly different method. Add-on interest means that the interest is added to the principal amount upfront, and the total is divided by the number of months. Here's how you can calculate it:
Total Interest = (Sticker Price + Rebates) * Interest Rate
Total Interest = ($42,500 + $5,100) * 0.025
Principal Amount = Sticker Price + Rebates
Principal Amount = $42,500 + $5,100
Total Amount to be Financed = Principal Amount + Total Interest
Total Amount to be Financed = $42,500 + $5,100 + ( $47,600 * 0.025 )
Monthly Payment = Total Amount to be Financed / Number of Months
Monthly Payment = $47,600 / 60
Using a calculator, you can find that the monthly payment at a 2.5% add-on interest rate is $793.33 (rounded to the nearest cent).
(c) To use the APR formula to find the APR for part (b), you need to rearrange the formula and solve for the APR:
APR = (Total Interest / Principal Amount) * (Number of Months / (Number of Months - 1)) * 100
Using the information from part (b), you can substitute the values into the formula:
APR = ($47,600 / $47,600) * (60 / (60 - 1)) * 100
Simplifying the equation:
APR = 1 * (60 / 59) * 100
Using a calculator, you can find that the APR is approximately 2.7% (rounded to one decimal place).
(d) Comparing the options, we see that the 0% APR option is preferable because it does not involve any interest charges. This means that the monthly payment will be lower than the one with the 2.5% add-on rate. So, the 0% APR is the preferred choice.