Holly wants to accumulate $$39,000$ in a fund with payments of $$1,800$ made at the end of every month. The interest rate is $5\mathrm{.}54\%$ compounded monthly.

a$.$ How many payments $($rounded up to the next payment$)$ will it take to accumulate this amount?

$25$ payments

$15$ payments

$20$ payments

$21$ payments

b$.$ How long will it take to accumulate this amount?

$3$ years and $9$ months

$3$ years and $3$ months

$4$ years and $9$ months

$1$ years and $9$ months