Katie plans to purchase a new car. She decides to borrow $$25,000$ from her friend at $8\%$ per year

compounded monthly for $4$ years. She plans to repay the loan with $48$ equal monthly payments.

a$.$ How much is the monthly payment?

b$.$ How much interest is in the $23$rd payment?

c$.$ What is the remaining balance immediately after she made her $37$ th payment?

d$.$ Later, she became able to pay off the loan at the end of the $30$th month. She has not yet made the

payment due at that month. What is the payoff amount for her loan at that time?