question$4$ Megan wants to accumulate $$34,000$ in a fund with payments of $$2,000$ made at the end of every month. The interest rate is $5\mathrm{.}33\%$ compounded monthly.

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

$23$ payments

$13$ payments

$16$ payments

$17$ payments

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

$3$ years and $5$ months

$4$ years and $3$ months

$4$ years and $5$ months

$1$ years and $5$ months