Lyle O'Keefe invests $$30,000$ at $8\%$ annual interest, leaving the money invested without withdrawing any of the interest for $8$ years. At the end of the $8$ years, Lyle withdrew the accumulated amount of money.

Instructions

$($a$)$ Compute the amount Lyle would withdraw assuming the investment earns simple interest.

$($b$)$ Compute the amount Lyle would withdraw assuming the investment earns interest compounded annually.

$($c$)$ Compute the amount Lyle would withdraw assuming the investment earns interest compounded semiannually

$6.$ Sally Medavoy will invest $$8,000$ a year for $20$ years in a fund that will earn $12\%$ annual interest. If the first payment into the fund occurs today, what amount will be in the fund in $20$ years? If the first payment occurs at year$-$end, what amount will be in the fund in $20$ years?

$7.$ Steve Madison needs $$250,000$ in $10$ years. How much must he invest at the end of each year, at $11\%$ interest, to meet his needs?