Tim Worker buys a new sofa for $629.95. He pays 25% down and takes an installment loan to complete the purchase. He makes 12 payments which include his principal and a $60.00 finance charge. What is the APR on his loan to the nearest tenth?
The down payment is $
The amount financed is $
The monthly payment will be $
At the end of one year the monthly payments will total $
The finance charge for one year ÷ amount financed is
To find the down payment, we can calculate 25% of the total cost of the sofa:
Down payment = 25% x $629.95 = $157.49
Therefore, the down payment is $157.49.
To calculate the amount financed, we need to subtract the down payment from the total cost of the sofa:
Amount financed = Total cost of the sofa - Down payment
Amount financed = $629.95 - $157.49 = $472.46
Therefore, the amount financed is $472.46.
To determine the monthly payment, we divide the total amount financed by the number of payments:
Monthly payment = Amount financed / Number of payments
Monthly payment = $472.46 / 12 = $39.37
Therefore, the monthly payment will be $39.37.
To find the total amount paid at the end of one year, we multiply the monthly payment by the number of payments:
Total amount paid in one year = Monthly payment x Number of payments
Total amount paid in one year = $39.37 x 12 = $472.44
Therefore, the total monthly payments will amount to $472.44 in one year.
Lastly, to calculate the annual percentage rate (APR), we need to calculate the finance charge for one year and then divide it by the amount financed:
Finance charge for one year ÷ Amount financed = APR
The finance charge for one year is given as $60.00.
APR = $60.00 ÷ $472.46 = 0.127 or 12.7% (rounded to the nearest tenth)
Therefore, the APR on Tim Worker's loan is 12.7% to the nearest tenth.
I = Po*r*t = $60.
472.46*r*1 = 60
r = 0.127 = 12.7% = APR
0.25 * 629.95 = $157.49 = Down payment.
629.95 - 157.49 = $472.46=Amt. financed.
(472.46+60)/12 = 532.46/12 = $44.37/mo.
472.46 + 60 = $532.46 = Total paid.