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- To find the monthly payment if financed for 60 months at 0% APR, we can use the formula for calculating the monthly payment for a loan:
Monthly Payment = Total Loan Amount / Number of Months
In this case, the Total Loan Amount is the sticker price minus the rebates, which is $42,650 - $5,100 = $37,550.
Therefore, the monthly payment is $37,550 / 60 = $625.83 (rounded to the nearest cent).
b- To find the monthly payment if financed at 2.5% add-on interest for 60 months, we need to calculate the Total Interest Paid and add it to the Total Loan Amount. Then, we can divide the sum by the Number of Months.
Total Interest Paid = Total Loan Amount * Interest Rate
= $37,550 * 2.5% = $938.75
Total Loan Amount + Total Interest Paid = $37,550 + $938.75 = $38,488.75
Monthly Payment = $38,488.75 / 60 = $641.48 (rounded to the nearest cent).
c- To use the APR approximation formula, we need to rearrange the formula to solve for the APR:
APR = [(Monthly Payment * Number of Months) / Total Loan Amount - 1] * 12 / Number of Months
In this case, the Monthly Payment is $641.48, the Number of Months is 60, and the Total Loan Amount is $37,550.
Substituting these values into the formula:
APR = [(641.48 * 60) / 37,550 - 1] * 12 / 60
APR = [(38,488.80 / 37,550) - 1] * 12 / 60
APR = (1.0269 - 1) * 12 / 60 = 0.0212 or 2.12% (rounded to the nearest hundredth).
d- In terms of which option, 0% APR or 2.5% add-on rate, should be preferred, it depends on your financial situation and priorities.
If you focus on immediate monthly payments and want to avoid paying any interest, then the 0% APR option would be preferred. However, keep in mind that you may not be eligible for any additional rebates or discounts by choosing this option.
On the other hand, if you are comfortable with paying interest and prefer smaller upfront costs (due to the rebate), the 2.5% add-on rate option would be preferred. Though it does come with an additional cost in terms of interest payments over the loan term.