$16.($a$)$ Calculate the time in days for RM$6,000$ to accumulate to RM$7,600$ at:

$($i$)$ an effective rate of interest of $1\%$ per quarter

$($ii$)$ a force of interest of $5\%$ per annum

$($iii$)$ a nominal rate of discount of $4\%$ per annum convertible every three months.

Note: You should assume there are $365$ days in a year.

$($b$)$ Calculate the effective rate of interest per half$-$year which is equivalent to a force of

interest of $3\%$ per annum.