Samuel bought a house with a mortgage of $$379,400.$ The mortgage is being financed with an interest

rate of $3\mathrm{.}76\%$ compounded monthly. Samuel will make payments of $$1,342.$

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

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

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