Problem $5$

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.

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 $65?$

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.

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.

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?

$($Retirement Analysis$)$

INPUT DATA

Part A$.$

Value of Gift $-$ PV

IRA Investment Annuity $-$ PMT

Years Working $-$ nper $1$

Annual Return While Working $-$ rate $1$

Part B$.$

Years Retired

Months Retired $-$ nper $2$

Annual Return While Retired

Monthly Return While Retired $-$ rate $2$

Part C$.$

Number of Children

Amount per child

Total Inheritance $-$ FV

SOLUTIONS

Part A $-$ Amount Available for Retirement

$=$FV$($rate$,$nper,pmt$,$pv$,$type$)$

Retirement Funds $-$ FV $=$

Part B $-$ Monthly Retirement Income

$=$PMT$($rate$,$nper,PV$,$fv$,$type$)$

Monthly Retirement Income $-$ PMT $=$

Part C $-$ Amount for Children's Inheritance

$=$PV$($rate$,$nper,pmt$,$fv$,$type$)$

Amount Set Aside at Retirement $-$ PV

Part D $-$ Retirement income After Inheritance

Original Retirement Funds

Less: Amount for Children

Net Retirement Funds $-$ PV

$=$PMT$($rate$,$nper,PV$,$fv$,$type$)$

Revised Monthly Income $-$ PMT

Monthly drop in Retirement Income