Question

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? A. 29.09% B. 68.75% C. 14.55% D. 34.38%
I know I'm making this harder than it needs to be, but I really don't understan. Can you please explain how to get the answer? Thanks!!!

Answer 1

Answer: option C. 14.55%

Explanation:

1) Total payments done:

Down payment + 10×montly payments = $20 + 10×$34 = $20 + $340 = $360

2) Interest paid

Total payments - original price = $360 - $320 = $40

3) Financed amount

Original price - down payment = $320 - $20 = $300

3) Percent interest

(Interest paid / financed amount ) × 100 = ($40 / $300) × 100 = 13.33%

4) Yearly rate

number of months in a year: 12

number of months to pay: 10 + 1 = 11

⇒ (Percent interest / 11) × 12 = (13.33% / 11) × 12 = 14.54%

Note that it has been assumed that the first monthly payment was made one month after the purchase, which leads to a total payment time of 11 months, that is why the divisor (denominator of the fraction is 11 and not 10).

Answer 2

IN finding the interest we need to use the following formula:
 Interest= Principal x Rate x Time  or I= PRT
Substitute values: I= [$20 + ($10 x $34)] -320 =$40
P= $320
R=?
T=10 months/year
I=PRT
Since R is a missing term, we will solve for R using this formula: R=I/PT
R=  [$20 + ($10 x $34)-320] / ($320 x 10 months)
                                          T=10 months÷12 months=0.83
R= ($40)/ $320 X 0.83
R= 40/ 265.6
R=15.06024096