Question

Karen uses her credit card to purchase a new television for $695.20. She can pay off up to $325 per month. The card has an annual rate of 17.9% compounded monthly. How much will she pay in interest?



$6.28



$16.96



$20.44



$62.16

Answer 1

Answer:  $ 16.96      

Step-by-step explanation:

Here, the present value of the loan, PV = $695.20

Annual Interest rate = 17.9%

⇒ Monthly interest rate = 17.9/12 = 1.41666666667

Thus, the monthly interest rate (decimal ) , r = 0.014167 ( approx)

Monthly payment, P = $ 325

Let the time period of the loan = n.

Since, $P= \frac{r(PV)}{1-(1+r)^{-n}}$

⇒ $325= \frac{0.014167(695.20)}{1-(1+0.014167)^{-n}}$

⇒  $1-(1+0.014167)^{-n}= \frac{10.37008984}{325}$

⇒ $1-(1+0.014167)^{-n}= 0.03190796873$

⇒  n = 2.19

Thus, her total payment = 2.19 × 325 =  711.75

⇒ Her total interest = 711.75 - 695.20 = $16.55

Since only 16.96 is near to 16.55

Thus, second option is correct.