Use PMT $=\frac{-\left(\frac{1}{n}\right)}{1-{(1+\frac{1}{n})}^{-nt}}$ to determine the regular payment amount, rounded to the nearest dollar, Your credit card
has a balanoe of $\mathrm{\$}4900$ and an annual interest rate of $17\mathrm{\%}$. With no further purchases charged to the card and the balanoe being paid off over five years, the monthly payment is $122, and the total interest paid is $2420. You can get a bank loan at $9.5\mathrm{\%}$ with a term of six years. Complete parts (a) and (b) bolow.
a. Hiow much wil you pay gach month? How does this compare with the credit-card payment each month? Select the correct choice below and fill in the answer boxes to complete your choice.
(Do not round until the tinal answer. Then round to the nearest dollar as needed.)
A. The monthly payments for the bank loan are approximately $\mathbf{s}$. This is $\mathbf{s}$ more than the monthy credilcard payments.
8. The monthly payments for the bank loan are approximately $\mathrm{\$}$. This is $\mathrm{\$}$ less than the monthly creditcard payments.

Step 1 ：Given that the principal amount of the bank loan is $4900, the annual interest rate is 9.5%, and the term of the loan is 6 years, we can use the PMT formula to calculate the monthly payment for the bank loan.

Step 2 ：Substitute the given values into the PMT formula: PMT $=\frac{-\left(\frac{1}{n}\right)}{1-{(1+\frac{1}{n})}^{-nt}}$, where n is the number of payments per year (12 for monthly payments), t is the term of the loan in years, and i is the annual interest rate divided by n.

Step 3 ：Calculate the monthly payment for the bank loan to be approximately $90. This is the amount that will need to be paid each month in order to pay off the loan over a period of 6 years.

Step 4 ：Compare this with the monthly payment for the credit card, which is given as $122. Subtract the bank loan monthly payment from the credit card monthly payment to find the difference.

Step 5 ：Calculate the difference between the monthly payment for the credit card and the bank loan to be $32.Thismeansthatthemonthlypaymentforthebankloanis$32 less than the monthly payment for the credit card.

Step 6 ：Final Answer: The monthly payments for the bank loan are approximately $\boxed{{\displaystyle 90}}$. This is $\boxed{{\displaystyle 32}}$ less than the monthly credit card payments.