vacuum cleaner was purchase on the installment plan with 12 monthly payments $36.98 each. If the cash price was $415 and there was no down payment , find the annual percentage rate.
36.98 * 12 = 443.76
443.76 - 415 = 39.76
I = PRT
39.76 = 415R
0.0958 = 9.58% = R
To find the annual percentage rate (APR) for the vacuum cleaner purchased on an installment plan, we can use the formula:
APR = (Total interest paid / Cash price) × (12 / Number of months)
First, let's calculate the total interest paid over the 12-month installment period.
Total interest paid = (Total payments - Cash price)
Total payments = 12 monthly payments × $36.98 each = $443.76
Total interest paid = $443.76 - $415 = $28.76
Now, we can calculate the APR using the formula:
APR = ($28.76 / $415) × (12 / 12)
APR = 0.0693 × 1
APR ≈ 0.0693 or 6.93% (rounded to two decimal places)
Therefore, the approximate annual percentage rate for the vacuum cleaner purchase on the installment plan is 6.93%.
To find the annual percentage rate (APR) for the vacuum cleaner purchased on the installment plan, with 12 monthly payments of $36.98 each and no down payment, we can use the following steps:
Step 1: Calculate the total amount paid.
The total amount paid over the 12 monthly payments can be calculated by multiplying the monthly payment by the number of payments:
Total amount paid = Monthly payment * Number of payments
Total amount paid = $36.98 * 12
Total amount paid = $443.76
Step 2: Calculate the finance charge.
The finance charge can be calculated by subtracting the cash price of the vacuum cleaner from the total amount paid:
Finance charge = Total amount paid - Cash price
Finance charge = $443.76 - $415
Finance charge = $28.76
Step 3: Calculate the APR.
The APR represents the annual cost of borrowing, expressed as a percentage. To calculate it, we need to determine the APR based on the finance charge and the cash price.
APR = (Finance charge / Cash price) * (12 / Number of payments) * 100
APR = ($28.76 / $415) * (12 / 12) * 100
APR ≈ 0.0692891566 * 1 * 100
APR ≈ 6.93
Therefore, the annual percentage rate (APR) for the vacuum cleaner purchased on the installment plan is approximately 6.93%.