a credit card holder owes $5,498 on a credit card with a 26.99% interest rate compounded monthly. assuming…

a credit card holder owes $5,498 on a credit card with a 26.99% interest rate compounded monthly. assuming no additional purchases are made with the card, what is the monthly payment the cardholder should make to pay off the debt in 5 years? round your answer to the nearest penny. a spreadsheet was used to calculate the correct answer. your answer may vary slightly depending on the technology used. $91.63 $123.66 $167.85 $215.29

a credit card holder owes $5,498 on a credit card with a 26.99% interest rate compounded monthly. assuming no additional purchases are made with the card, what is the monthly payment the cardholder should make to pay off the debt in 5 years? round your answer to the nearest penny. a spreadsheet was used to calculate the correct answer. your answer may vary slightly depending on the technology used. $91.63 $123.66 $167.85 $215.29

Answer

Explanation:

Step1: Identify the formula for monthly payment

The formula for the monthly payment of a loan is (M = P\times\frac{r(1 + r)^n}{(1 + r)^n-1}), where (P) is the principal amount, (r) is the monthly interest rate, and (n) is the total number of payments.

Step2: Calculate the values of (P), (r), and (n)

  • (P=$5498)
  • The annual interest rate (i = 26.99%=0.2699). The monthly interest rate (r=\frac{0.2699}{12}\approx0.0225)
  • The number of years (t = 5). The total number of payments (n=5\times12 = 60)

Step3: Substitute the values into the formula

[ \begin{align*} M&=5498\times\frac{0.0225(1 + 0.0225)^{60}}{(1+ 0.0225)^{60}-1}\ \end{align*} ] First, calculate ((1 + 0.0225)^{60}). Let (x=(1 + 0.0225)^{60}). Using the formula (a^b=e^{b\ln(a)}), (\ln(1.0225)\approx0.02225), (b = 60), so (x=e^{60\times0.02225}\approx e^{1.335}\approx3.8)

[ \begin{align*} M&=5498\times\frac{0.0225\times3.8}{3.8 - 1}\ &=5498\times\frac{0.0855}{2.8}\ &=5498\times0.0305357\ &\approx167.85 \end{align*} ]

Answer:

C. ($167.85)