$5-36.$ Suppose that you were to receive a $$30,000$ gift upon graduation from

your master's degree program, when you turn $31$ years old. At the end of

each working year for $34$ years, you put an additional $$5,000$ into an IRA.

a$.$ Assuming you earn an annual compounded rate of $7\mathrm{.}5$ percent on the

gift and the IRA investments, how much would be available when you

retire at age $65?$

b$.$ If you hope to draw money out of that investment at the end of every

month for $30$ years following retirement, how much could you withdraw

each month? Assume that during the years you are retired the money

earns an annual rate of $6$ percent compounded monthly.

c$.$ You realize that if you draw out that amount each month there will be

nothing left for your two children. You decide that you want to leave

$$250,000$ to each of your children $30$ years after you retire. How much

would you have to invest at your retirement to fund your children's

inheritance? Assume that you will earn $7\mathrm{.}5$ percent compounded

annually on the money invested for your children.

d$.$ If you set aside the money for your children, how much could you draw

out each month during your retirement if you can earn $6$ percent per

annum compounded monthly on the portion that is not set aside for the

children?

$5-37.$ Old School is trying to decide whether it should purchase or lease a

new high$-$speed photocopier machine. It will cost the school $$14,000$ to