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

Question

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.

Assuming you earn an annual compounded rate of 7.5 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 7.5 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?

Explanation / Answer

1) Amount available at the age of 65 is the sum of following future values: FV of the gift of 30000 = 30000*1.075^34 = $ 3,50,759.17 FV of the annuity of 5000 deposited yearly = 5000*(1.075^34-1)/(0.075*1.075^34) = $     60,964.75 Amount available at the retirment age of 65 $ 4,11,723.92 Answer 2) Amount drawn at the end of each month for 30 years after retirement {interest rate = 6%/12 = 0.5% per month, number of months = 30*12 = 360) using the formula to find annuity when its PV is given. The PV is $411723.92. Monthly instalment = 411723.92*0.005*1.005^360/(1.005^360-1) = $        2,468.49 Answer 3) The total amount to be accumulated for the two children = 250000*2 = $500,000, being the FV. Amount to be invested now, at monthly interest of 7.5%/12 = 0.625% = 500000/1.00625^300 = $     77,126.21 Answer 4) Amount that will be set aside for self at the age of 65 = 411723.92-77126.21 = 334597.71 Amount that can be withdrawn monthly at 0.5% interest compounded monthly = 334597.71*0.005*1.005^300/(1.005^300-1) = $        2,155.82 Answer

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