$3.$ Equal end$-$of$-$year payments of $$263\mathrm{.}80$ each are being made on a $$1\mathrm{.}000$ loan at $12\%$ effective interest per year.

a$.$ How many payments are required to repay the entire loan?

b$.$ Immediately after the second payment, what lump$-$sum amount would completely pay off the loan?