Joe Summers buys a gas grill and accessories. The cost, including tax, amounts to $850.00. Joe finances the grill over 12 months after making a $150 down payment. The true annual interest rate is 14%. What are Joe's monthly payments (principal plus interest)?
To the nearest penny, c = $
.
Total of payments = amount financed + c = $
.
Total of payments ÷ number of payments = monthly payment = $
.
850 - 150 = 700 owed
1.14 * 700 = 798 total payments in 12 months
798 / 12 = $ 66.50
To calculate Joe's monthly payments, we need to find the amount financed and then use the formula for calculating the monthly payment for a loan.
Step 1: Calculate the amount financed
The amount financed is the total cost minus the down payment. In this case, the total cost including tax is $850.00 and the down payment is $150.00. So, the amount financed is:
Amount financed = $850.00 - $150.00 = $700.00
Step 2: Calculate the total amount of payments (principal plus interest)
The true annual interest rate is given as 14%. However, we need to convert this to a monthly interest rate. To do this, divide the annual interest rate by the number of months in a year:
Monthly interest rate = 14% ÷ 12 = 0.14 ÷ 12 = 0.0117 (approximately)
Now, we can calculate the total amount of payments using the formula:
Total amount of payments = Amount financed + (Amount financed x Monthly interest rate x Number of months)
Total amount of payments = $700.00 + ($700.00 x 0.0117 x 12)
Total amount of payments = $700.00 + $97.56
Total amount of payments = $797.56
Step 3: Calculate the monthly payment
To find the monthly payment, divide the total amount of payments by the number of months in the loan:
Monthly payment = Total amount of payments ÷ Number of payments
Monthly payment = $797.56 ÷ 12
Monthly payment = $66.46 (rounded to the nearest penny)
So, Joe's monthly payment (principal plus interest) is approximately $66.46.
First, let's calculate the amount financed by subtracting the down payment from the total cost:
Amount Financed = Total Cost - Down Payment
= $850.00 - $150.00
= $700.00
Next, let's calculate the total amount Joe will pay over the 12 months:
Total Payments = Amount Financed + c
Where "c" is the total interest paid.
To find "c", we can use the formula:
c = Amount Financed * Annual Interest Rate * (Number of Months / Number of Months in a Year)
c = $700.00 * 0.14 * (12 / 12)
c = $117.60
Therefore,
Total Payments = Amount Financed + c
= $700.00 + $117.60
= $817.60
Finally, let's calculate the monthly payment by dividing the total payments by the number of months:
Monthly Payment = Total Payments / Number of Payments
= $817.60 / 12
= $68.13 (rounded to the nearest penny)
Therefore, Joe's monthly payment will be approximately $68.13.