Question

1a) Today is your 22nd birthday. Suppose you decide to start saving $15,000 annually for retirement, with the first deposit being made one year from today. You expect to earn a return of 9 percent per year on this money. Considering that you plan to retire 28 years from today and that you expect to live for 30 years after retirement, how much can you spend each year after you retire? You will be able to withdraw your first amount at the end of your first retirement year.

1b) Suppose that you just had your first baby, Oprah, and you wish to ensure that enough money will be available to pay for Oprah's college education. Tuition and other fees today add up to $12,500 per year. Tuition and other costs are expected to increase at a rate of 4 percent per year.

Assuming that all of Oprah's college savings are invested in an account paying 7 percent interest, then the amount of money she will need to have available at age 18 to pay for all four years of her undergraduate education is closest to...?

Answer 1

Part-1 , Calculate how much can you spend each year after you retire?

First, we will calculate corpus available after 28 years by investing $15000 annually at 9%

At the Age	Opening	Fresh Investment	Interest on Opening Balance	Closing Balance
23	$                       -	$ 15,000.00	$       1,350.00	$       16,350.00
24	$       16,350.00	$ 15,000.00	$       2,821.50	$       34,171.50
25	$       34,171.50	$ 15,000.00	$       4,425.44	$       53,596.94
26	$       53,596.94	$ 15,000.00	$       6,173.72	$       74,770.66
27	$       74,770.66	$ 15,000.00	$       8,079.36	$       97,850.02
28	$       97,850.02	$ 15,000.00	$     10,156.50	$    1,23,006.52
29	$    1,23,006.52	$ 15,000.00	$     12,420.59	$    1,50,427.11
30	$    1,50,427.11	$ 15,000.00	$     14,888.44	$    1,80,315.55
31	$    1,80,315.55	$ 15,000.00	$     17,578.40	$    2,12,893.95
32	$    2,12,893.95	$ 15,000.00	$     20,510.46	$    2,48,404.40
33	$    2,48,404.40	$ 15,000.00	$     23,706.40	$    2,87,110.80
34	$    2,87,110.80	$ 15,000.00	$     27,189.97	$    3,29,300.77
35	$    3,29,300.77	$ 15,000.00	$     30,987.07	$    3,75,287.84
36	$    3,75,287.84	$ 15,000.00	$     35,125.91	$    4,25,413.74
37	$    4,25,413.74	$ 15,000.00	$     39,637.24	$    4,80,050.98
38	$    4,80,050.98	$ 15,000.00	$     44,554.59	$    5,39,605.57
39	$    5,39,605.57	$ 15,000.00	$     49,914.50	$    6,04,520.07
40	$    6,04,520.07	$ 15,000.00	$     55,756.81	$    6,75,276.88
41	$    6,75,276.88	$ 15,000.00	$     62,124.92	$    7,52,401.79
42	$    7,52,401.79	$ 15,000.00	$     69,066.16	$    8,36,467.96
43	$    8,36,467.96	$ 15,000.00	$     76,632.12	$    9,28,100.07
44	$    9,28,100.07	$ 15,000.00	$     84,879.01	$ 10,27,979.08
45	$ 10,27,979.08	$ 15,000.00	$     93,868.12	$ 11,36,847.20
46	$ 11,36,847.20	$ 15,000.00	$ 1,03,666.25	$ 12,55,513.44
47	$ 12,55,513.44	$ 15,000.00	$ 1,14,346.21	$ 13,84,859.65
48	$ 13,84,859.65	$ 15,000.00	$ 1,25,987.37	$ 15,25,847.02
49	$ 15,25,847.02	$ 15,000.00	$ 1,38,676.23	$ 16,79,523.25
50	$ 16,79,523.25	$ 15,000.00	0	$ 16,94,523.25

Hence, funds available on 50th Birthday will be $ 16,94,523.25

From this money, I will buy an annuity for 30 years

Lets assume periodic annual payment be "P", the present value of annuity payment will be as follows

PV of Annuity = P*PVAF(9%,30Years)

$1694523.25 = P*10.2737

P = $1694523.25/10.2737

P = $13,30,394.33

Part-2 Calculate amount of money oprah need to have available at age 18 to pay for all four years of her undergraduate education

Funds Required at the begining of under graduate year are as follows :

Graduation Year	PV	Inflation	Period Elapsed	FV = PV*(1+r)^n
1	$ 12,500.00	4%	18	$ 25,322.71
2	$ 12,500.00	4%	19	$ 26,335.61
3	$ 12,500.00	4%	20	$ 27,389.04
4	$ 12,500.00	4%	21	$ 28,484.60

Therefore, in the first year of graduation Oprah need $ 25322.71 , 2nd year - $26355.61, 3rd Year - $27389.04 and 4th Year $28484.60

Now to calculate the amount of money required at the age of 18th year, we must calculate the Present Value of fees required to be paid at 7% rate of return

Amount Required at the Age of 18 = PV of 1st Year Fee + PV of 2nd Year Fee + PV of 3rd Year Fee + PV of 4th Year Fee

Amount Required at the Age of 18 = $ 25,322.71 +  $ 26,335.61*PVF(7%,1Year) + $27389.04*PVF(7%,2Year) + $28484.60*PVF(7%,3Year)

Amount Required at the Age of 18 = $ 25,322.71 +  $ 26,335.61*.935 + $27389.04*.873 + $28484.60*.816

Amount Required at the Age of 18 = $ 97100.57