Fina 440 makeup test Time Value of Money Morica is 35 years old, and would Ike t

Question

Fina 440 makeup test Time Value of Money Morica is 35 years old, and would Ike to routine at age 65 (30 year from today) Her goal is have enough in her account to provide an income of $75 000 a year starting a year after retirement or year 31, for 25 years Here after She had a late start on saving for retirement, with a current balance of $10,000 To catch up she .s new committed to saving $400 a month He first contribution a month from row A single parent with two children, both of which will be attending college starting in five years, she won't be able to increase the $400 until after the kids have graduated Once He Children are finished with college she will have extra disposable income but is worried about just how much of an increase it will take to meet her ultimate retirement goals. To help her meet this goal estimate how much she will need to save every month, starting 10 years from now, when the loads are out of college Assume an average annual 7% return m the retirement account. In addition, she would like to help her loads at a modest level She would like to be able to give them each $4000 a year for four years starting in five years She would use a tax account that is earring 5. 25 percent a year on She wants to know how much she would have to deposit monthly in this account to reach this goal.

Explanation / Answer

1) To organize and summarize this information, we will need her three cash inflows to be the equivalent of her one cash outflow.

1.The money already in the account is the first inflow.
2. The money to be saved during the next 10 years is the second inflow.
3. The money to be saved between years 11 and 30 is the third inflow.
4.The money to be taken as income from years 31 to 50 is the one outflow.

All amounts are given to calculate inflows 1 and 2 and the outflow. The third inflow has an unknown annuity amount that will need to be determined using the other amounts. We start by drawing a timeline and specifying that all amounts be indexed at t = 30, or her retirement day.

Next, calculate the three amounts for which we have all the necessary information, and index to t = 30.

(inflow 1) FV (single sum) = PV *(1 + r)N = ($10,000)*(1.07)30 = $76,123
(inflow 2) FV annuity factor = ((1 + r)N - 1)/r = ((1.07)10 - 1)/.07 = 13.8571

With a $4800 payment, FV (annuity) = ($4800)*(13.8571) = $66,514

This amount is what is accumulated at t = 10; we need to index it to t = 30.

FV (single sum) = PV *(1 + r)N = ($66,514)*(1.07)20 = $257,409

(cash PV annuity factor = (1 - (1/(1 + r)N)/r = (1 - (1/(1.07)25/0.07 = 11.6548277.outflow)

With payment of $75,000, PV (annuity) = ($75,000)*(11.6548277) = $874,112.

Since the three cash inflows = cash outflow, we have ($66,514) + ($257,409) + X = $874,112, or X = 550,189 at t = 30. In other words, the money she saves from years 11 through 30 will need to be equal to $550,189 in order for her to meet retirement goal.

FV annuity factor = ((1 + r)N - 1)/r = ((1.07)20 - 1)/.07 = 41

A = FV/FV annuity factor = (550,189)/41 = $13,419

We find that by increasing the annual savings from $4800(400 per month) to $13,419 starting in year 11 and continuing to year 30, she will be successful in accumulating enough income for retirement.

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