find the APR to the nearest half percent, for the following data. purchase price $3500, down payment $500, add-on interest rate 7%, # of payments 18
To find the APR (Annual Percentage Rate) for the given data, we need to follow a few steps:
Step 1: Subtract the down payment from the purchase price.
Purchase price after down payment = $3500 - $500 = $3000
Step 2: Calculate the total interest paid over the loan term.
Total interest = Purchase price * Add-on interest rate * Number of payments
= $3000 * 7% * 18
= $3780
Step 3: Determine the total amount paid over the loan term (purchase price + total interest).
Total amount paid = Purchase price + Total interest
= $3000 + $3780
= $6780
Step 4: Calculate the monthly payment.
Monthly payment = Total amount paid / Number of payments
= $6780 / 18
= $376.67 (rounded to 2 decimal places)
Step 5: Determine the nominal interest rate.
Nominal interest rate = (Total amount paid - Purchase price) / Purchase price
= ($6780 - $3000) / $3000
= 1.26 (or 126%)
Step 6: Convert the nominal interest rate to APR, rounding to the nearest half percent.
APR = Nominal interest rate / Number of payments
= 1.26 / 18
= 0.07 (rounded to 2 decimal places)
= 7% (to the nearest whole percent)
Therefore, the APR for the given data is 7% to the nearest half percent.