Question $7(12$ points$)$

Assume that the annual interest rate is $8\%.$ Compute

$($i$)$ The future value of $30,000$ invested today for a period of $4$ years, if the interest rate is compounded monthly.

$($ii$)$ The present value today of $50,000$ received after $5$ years, if the interest rate is compounded every $6$ months.