A newlywed couple bought a washer and dryer for $800. They paid 5% down and then paid 12 monthly payments of $65.41. Determine the APR of the loan to the nearest tenth of a percent.
Po = 800 - 0.05*800 = $760
P = 65.41/mo. * 12mo. = $784.92
I = P-Po = 784.92 - 760 = $24.92
%I = (I/Po)*100% = (24.92/760)*100% =
3.3 = APR.
To determine the APR (Annual Percentage Rate) of the loan, we need to calculate the total amount paid by the couple over the course of one year, expressed as a percentage of the total amount financed.
First, let's calculate the down payment they made. The purchase price of the washer and dryer is $800, and they paid 5% down. So, the down payment amount is 5% of $800, which is:
Down payment = 5% of $800 = 0.05 * $800 = $40
Now, let's calculate the total amount financed. It is the purchase price minus the down payment:
Total amount financed = Purchase price - Down payment = $800 - $40 = $760
Next, we need to calculate the total amount paid by the couple over 12 monthly payments of $65.41. The equation for a monthly payment can be written as:
Total amount paid = Monthly payment * Number of payments
Substituting the values into the equation, we get:
Total amount paid = $65.41 * 12 = $784.92
Finally, let's calculate the interest paid over one year. It is the difference between the total amount paid and the total amount financed:
Interest paid = Total amount paid - Total amount financed
= $784.92 - $760
= $24.92
Now, to calculate the APR, we divide the interest paid by the total amount financed and multiply by 100 to express it as a percentage:
APR = (Interest paid / Total amount financed) * 100
= ($24.92 / $760) * 100
= 3.276315 * 100
≈ 3.3%
Therefore, the APR of the loan to the nearest tenth of a percent is approximately 3.3%.