Hillary is leasing a car originally valued at $$44,880.$ The lease is being financed with an interest rate of

$7\mathrm{.}93\%$ compounded monthly with beginning of month payments of $$497.$

$($a$)$ How many payments will Hillary have to make to repay the original value?

payment$($s$)$

$($b$)$ How long, in months, will it take Hillary to pay off the lease? $($Hint: In an annuity due, payments are

made at the beginning of each period.$)$

month$($s$)$