A car with a sticker price of $42,200 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.)
$ 1
(b) Find the monthly payment if financed at 2.5% add-on interest for 60 months. (Round your answer to the nearest cent.)
$ 2
(c) Use the APR approximation formula to find the APR for part (b). (Round your answer to one decimal place.)
3 %
a.(42200-5100)/60 = $618.33 Per Month.
b. Po = 42200-5100 = Amount Financed.
P = (Po*r*t)/(1-(1+r)^-t)
r = (2.5%/12)/100% = 0.002083 = Monthly
% rate expressed as a decimal.
t = 60 months.
Plug the above values into the given Eq and get P = $39,505.80.
Monthly = P/60.
(a) To find the monthly payment if financed for 60 months at 0% APR, we need to calculate the total loan amount after deducting the rebates from the sticker price.
Total loan amount = Sticker price - Rebates
= $42,200 - $5,100
= $37,100
Since the APR is 0%, there will be no interest charged on the loan. Therefore, the monthly payment will be the total loan amount divided by the number of months:
Monthly payment = Total loan amount / Number of months
= $37,100 / 60
≈ $618.33
Therefore, the monthly payment if financed for 60 months at 0% APR is approximately $618.33.
(b) To find the monthly payment if financed at 2.5% add-on interest for 60 months, we need to use the following formula:
Monthly payment = (Loan amount + (Interest rate * Loan amount)) / Number of months
First, calculate the loan amount after deducting the rebates:
Loan amount = Sticker price - Rebates
= $42,200 - $5,100
= $37,100
Next, calculate the interest amount:
Interest amount = Interest rate * Loan amount
= 2.5% * $37,100
= $927.50
Now, calculate the total loan amount:
Total loan amount = Loan amount + Interest amount
= $37,100 + $927.50
= $38,027.50
Finally, calculate the monthly payment:
Monthly payment = Total loan amount / Number of months
= $38,027.50 / 60
≈ $633.79
Therefore, the monthly payment if financed at 2.5% add-on interest for 60 months is approximately $633.79.
(c) To find the APR using the APR approximation formula, we can use the following steps:
1. Calculate the finance charges:
Finance charges = Total loan amount - Loan amount
= $38,027.50 - $37,100
= $927.50
2. Calculate the monthly interest rate:
Monthly interest rate = Finance charges / Loan amount
= $927.50 / $37,100
≈ 0.025
3. Calculate the APR using the APR approximation formula:
APR = Monthly interest rate * 12
≈ 0.025 * 12
= 0.3 or 30%
Therefore, the APR for part (b) is approximately 3%.
To find the monthly payment for each scenario, we can use the formula for calculating the monthly payment on a loan:
Monthly Payment = Loan Amount / Number of Months
(a) For part (a), since the financing is at 0% APR, there is no interest charged on the loan. Therefore, the monthly payment will simply be the total financed amount divided by the number of months.
Step 1: Calculate the total financed amount
Total Financed Amount = Sticker Price - Rebates
Total Financed Amount = $42,200 - $5,100
Total Financed Amount = $37,100
Step 2: Calculate the monthly payment
Monthly Payment = Total Financed Amount / Number of Months
Monthly Payment = $37,100 / 60
Monthly Payment ≈ $618.33 (rounded to the nearest cent)
Therefore, the monthly payment for part (a) is approximately $618.33.
(b) For part (b), the loan is charged with a 2.5% add-on interest rate. The add-on interest rate is added to the loan amount upfront, and then the total amount is divided by the number of months to calculate the monthly payment.
Step 1: Calculate the total loan amount with interest
Total Loan Amount = Sticker Price - Rebates + (Add-On Interest * Loan Amount)
Total Loan Amount = $42,200 - $5,100 + (0.025 * $42,200)
Total Loan Amount ≈ $42,200 - $5,100 + $1,055
Total Loan Amount ≈ $38,155
Step 2: Calculate the monthly payment
Monthly Payment = Total Loan Amount / Number of Months
Monthly Payment = $38,155 / 60
Monthly Payment ≈ $635.92 (rounded to the nearest cent)
Therefore, the monthly payment for part (b) is approximately $635.92.
(c) To find the approximate APR for part (b), we can use the APR approximation formula:
APR = (2 * Add-On Interest Rate * 12) / (1 + Number of Payments * Add-On Interest Rate)
Step 1: Calculate the approximate APR
APR = (2 * 0.025 * 12) / (1 + 60 * 0.025)
APR ≈ 0.6 / 2.5
APR ≈ 0.24
Converting the decimal to a percentage, the approximate APR is 24.0%.
Therefore, the approximate APR for part (b) is 24.0%.