Jonathan wants to accumulate $$37,000$ in a fund with payments of $$1,000$ made at the end of every six months. The interest rate is $6\mathrm{.}39\%$ compounded semi$-$annually.

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

$29$ payments

$20$ payments

$24$ payments

$25$ payments

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

$14$ years and $6$ months

$15$ years and $3$ months

$14$ years and $6$ months

$12$ years and $6$ months