Patriciana bought a house with a mortgage of $$346,400.$ The mortgage is being financed with an interest

rate of $4\mathrm{.}85\%$ compounded monthly. Patriciana will make payments of $$1,878.$

$($a$)$ How many payments will Patriciana have to make to repay the mortgage?

payment$($s$)$

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

are made at the beginning of each period.$)$

month$($s$)$