Jordan wants to accumulate $$33,000$ in a fund with payments of $$1,600$ made at the end of every quarter. The interest rate is $5\mathrm{.}73\%$ compounded quarterly.

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

$23$ payments

$14$ payments

$18$ payments

$19$ payments

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

$6$ years and $9$ months

$7$ years and $3$ months

$7$ years and $9$ months

$4$ years and $9$ months