select the correct answer. seth is trying to pay off his credit card. he plans to pay it off in 24 months…
select the correct answer. seth is trying to pay off his credit card. he plans to pay it off in 24 months. interest on the card is compounded monthly at a fixed annual rate of 11.6%. seth currently has a balance of $18,875 on his credit card. use the formula for the sum of a finite geometric series to determine seths approximate monthly payment. $p=\frac{f_p(t)}{1-(1 + i)^{-n}}$ a. seths approximate monthly payment will be $868.35. b. seths approximate monthly payment will be $753.97. c. seths approximate monthly payment will be $884.99. d. seths approximate monthly payment will be $834.75.
Answer
Explanation:
Step1: Calculate the monthly interest rate
The annual interest rate is $11.6%=0.116$. The monthly interest rate $i=\frac{0.116}{12}\approx0.00967$.
Step2: Identify the number of periods
The number of months $n = 24$. The present - value of the loan $PV=18875$.
Step3: Substitute values into the formula
We use the formula $P=\frac{PV\times i}{1-(1 + i)^{-n}}$. Substituting $PV = 18875$, $i=0.00967$ and $n = 24$ into the formula: First, calculate $(1 + 0.00967)^{-24}$. Let $x=(1 + 0.00967)^{-24}=\frac{1}{(1 + 0.00967)^{24}}$. Using a calculator, $(1 + 0.00967)^{24}\approx1.2537$. So $x\approx\frac{1}{1.2537}\approx0.7977$. Then, $1-(1 + 0.00967)^{-24}=1 - 0.7977 = 0.2023$. $PV\times i=18875\times0.00967 = 182.52125$. $P=\frac{182.52125}{0.2023}\approx884.99$.
Answer:
C. Seth's approximate monthly payment will be $884.99.