A consumer loan you took out several years ago requires fixed monthly payments of $$700\mathrm{.}00.$ You just made a payment, and $29$ payments remain to be made; the next payment is due in one month. The rate of return used to compute these payments $($when the loan was granted$)$ was $21\%($APR$,$ compounded monthly$).$ Use annuity formulas to answer the questions below.

a$.$ What is the present value of the remaining payments, using the APR given above as a discount rate?

b$.$ Your friend, a bank loan officer, looked at your risk profile. She says that her bank would offer you a loan on similar terms but at a lower return: an annual return of $19\%($EAR$).$ Use that return to determine the present value of your future payments on the loan described above.

c$.$ Which of these two present values is the more accurate measure of the current value of those future payments? Explain your answer! $($Hint: this requires no calculations, just common sense.$)$