8. Noel Devine bought a new dishwasher for \( \$ 320 \). He paid \( \$ 20 \) down and made 10 monthly payments of \( \$ 34 \). What actual yearly interest rate did Noel pay?
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To find the actual yearly interest rate that Noel paid on his dishwasher, we first need to calculate the total amount he paid for it. He made a down payment of $20 and then paid $34 for 10 months, which totals to $340. Adding the down payment, the total cost is \( \$20 + (10 \times 34) = \$20 + \$340 = \$360 \). Next, we find the amount financed, which is the total cost minus the down payment: \( \$320 - \$20 = \$300 \). To find the interest paid, subtract the amount financed from the total amount paid: \( \$360 - \$320 = \$40 \). Now to find the interest rate, we can use the formula for the annual percentage rate (APR). The interest for one year on the principal amount can be found by taking the total interest ($40) divided by the principal ($300), multiplied by the number of periods (12 months for a year). This gives us \( \frac{40}{300} \times 12 \), which equals \( 0.16 \) or 16% for the year. Thus, the actual yearly interest rate that Noel paid is 16%.