you have a balance of $390 on your credit card and make no more charges. assume that the card carries an apr…

you have a balance of $390 on your credit card and make no more charges. assume that the card carries an apr of 17%. suppose you wish to pay off the card in six months by making equal payments each month. what is your monthly payment? (give your answer to the nearest cent.) monthly payment: $

you have a balance of $390 on your credit card and make no more charges. assume that the card carries an apr of 17%. suppose you wish to pay off the card in six months by making equal payments each month. what is your monthly payment? (give your answer to the nearest cent.) monthly payment: $

Answer

Explanation:

Step1: Calculate the monthly interest rate

The annual percentage rate (APR) is (17%=0.17). The monthly interest rate (r=\frac{0.17}{12})

Step2: Determine the number of payments

The number of months (n = 6)

Step3: Use the present - value of an ordinary annuity formula

The present - value of an ordinary annuity formula is (PV = PMT\times\frac{1-(1 + r)^{-n}}{r}), where (PV=$390) (the present value or the initial balance), (PMT) is the monthly payment, (r) is the monthly interest rate, and (n) is the number of payments.

We need to solve for (PMT). Rearranging the formula for (PMT) gives (PMT=\frac{PV\times r}{1-(1 + r)^{-n}})

Substitute (PV = 390), (r=\frac{0.17}{12}\approx0.014167), and (n = 6) into the formula:

[ \begin{align*} (1 + r)^{-n}&=(1+\frac{0.17}{12})^{-6}\ &=(1.014167)^{-6}\ &\approx0.91777 \end{align*} ]

[ \begin{align*} PMT&=\frac{390\times\frac{0.17}{12}}{1-(1.014167)^{-6}}\ &=\frac{390\times0.014167}{1 - 0.91777}\ &=\frac{5.52513}{0.08223}\ &\approx67.2 \end{align*} ]

Answer:

(67.20)