A new employee charged $\$ 2790$ on his credit card to relocate for his first job. After noticing that the interest rate for his balance was $21 \%$ compounded monthly, he stopped charging on that account. He wishes to pay off his balance in 3 years using automatic payments sent at the end of each month. a. What monthly payment must he make to pay off the account at the end of 3 years? b. How much total interest will he have paid? a. What monthly payment must he make to pay off the account at the end of 3 years? (Round to the nearest cent as needed.)

Step 1 ：Given that the principal amount (PV) is $2790, the annual interest rate is 21%, and the loan term is 3 years.

Step 2 ：First, we need to convert the annual interest rate to a monthly rate. This is done by dividing the annual rate by 12. So, \(r = \frac{21}{12} = 1.75%\) per month.

Step 3 ：Next, we need to convert the loan term from years to months. This is done by multiplying the number of years by 12. So, \(n = 3 \times 12 = 36\) months.

Step 4 ：We can now use the formula for the monthly payment of a loan: \(P = \frac{r \times PV}{1 - (1 + r)^{-n}}\)

Step 5 ：Substituting the given values into the formula, we get \(P = \frac{0.0175 \times 2790}{1 - (1 + 0.0175)^{-36}}\)

Step 6 ：Calculating the above expression, we find that the monthly payment he must make to pay off the account at the end of 3 years is approximately $105.11.

Step 7 ：\(\boxed{105.11}\)