Question

You have just graduated Binghamton University at age 22. You hard work has paid off as you already have a job as an investment banker at Goldman Sachs waiting for you. You plan to work continuously until age 65 and retire exactly on that day. You expect to live until exactly 90 and enjoy your golden years and leave you heirs NOTHING. Assume your investments earn 8% per year.

You plan to contribute $10,000 to your retirement fund every year on your birthday starting at age 23. Your last deposit will be at exactly age 65 and your first withdrawal will be at age 66. Your last withdrawal will be at the moment you die at age 90.

Ignore all tax considerations for this problem.

How much you will be able to spend each year in retirement?

FV (deposits) = PV (withdrawals)

NOTE: This could be at any time period but t=65 is particularly convenient

     

How much will you be able to spend each year in retirement if you begin deposits at age 30?

     

How much larger do your deposits have to be if deposits start at age 30 to equal your answer in part (i)?

Now let’s consider the effect of inflation.

The values calculated above are nominal values. What is more important is real, i.e. inflation-adjusted, values?

Assume inflation averages 4% per year.

Re-calculate parts (i), (ii) and (iii) above.

Comment on above.

show work

Answer 1

As per given case , 22 years old person got a job as Investment Banker and planning to invest $10000 from at the age of 23 until 65 years

Total No. of years = 42 Years

Rate of Interest = 8%

Total corpus at the age of 66 starting will be

                                                $10000(1+8%)⁴²

=   $ 3,285,830.05

So At the Age of 66 in initial he will have total corpus of $ 3,285,830.05.

Now if he wants to withdraw till age of 90 years means next 25 years he wants to withdraw as pension then from 66 years till 90 years he will be getting this pension $307,812.55 annually.

P= R (PV)/1-(1+R)^-n

P= Payment

Pv- Present value    R- Rate    n = No. of years

Annual Balances

Year	Beginning Balance	Interest Earned In the Period	Ending Balance
1.	$3,285,830.05	$262,866.40	$3,240,883.91
2.	$3,240,883.91	$259,270.71	$3,192,342.07
3.	$3,192,342.07	$255,387.37	$3,139,916.89
4.	$3,139,916.89	$251,193.35	$3,083,297.69
5.	$3,083,297.69	$246,663.82	$3,022,148.96
6.	$3,022,148.96	$241,771.92	$2,956,108.33
7.	$2,956,108.33	$236,488.67	$2,884,784.45
8.	$2,884,784.45	$230,782.76	$2,807,754.66
9.	$2,807,754.66	$224,620.37	$2,724,562.49
10.	$2,724,562.49	$217,965.00	$2,634,714.94
11.	$2,634,714.94	$210,777.20	$2,537,679.59
12.	$2,537,679.59	$203,014.37	$2,432,881.41
13.	$2,432,881.41	$194,630.51	$2,319,699.37
14.	$2,319,699.37	$185,575.95	$2,197,462.77
15.	$2,197,462.77	$175,797.02	$2,065,447.25
16.	$2,065,447.25	$165,235.78	$1,922,870.48
17.	$1,922,870.48	$153,829.64	$1,768,887.57
18.	$1,768,887.57	$141,511.01	$1,602,586.03
19.	$1,602,586.03	$128,206.88	$1,422,980.37
20.	$1,422,980.37	$113,838.43	$1,229,006.25
21.	$1,229,006.25	$98,320.50	$1,019,514.20
22.	$1,019,514.20	$81,561.14	$793,262.79
23.	$793,262.79	$63,461.02	$548,911.26
24.	$548,911.26	$43,912.90	$285,011.62
25.	$285,011.62	$22,800.93	$-0.00

If he start deposit from age of 30 years till 65. He will be able to invest for 35 Years

    $10000(1=8%)³⁵   = $ 1,861,021.48

Now let's consider Inflation @ 4 %

In case if he starts from the age of 23 then It corpus will be

   Future value after 65 years age=   $641,605.34

In case if he invests from 30 years age then Future value will be considering 4 % inflation $470,027.43

                                                      = (1+8)/(1+4) - 1

Now After completion of 65 Years when he wants to withdraw pension considering 4 % inflation

Total corpus will be $641,605.34

You can withdraw $60,104.80 annually.

Annual Balances

Year	Beginning Balance	Interest Earned In the Period	Ending Balance
1.	$641,605.34	$51,328.43	$632,828.96
2.	$632,828.96	$50,626.32	$623,350.47
3.	$623,350.47	$49,868.04	$613,113.71
4.	$613,113.71	$49,049.10	$602,058.00
5.	$602,058.00	$48,164.64	$590,117.83
6.	$590,117.83	$47,209.43	$577,222.46
7.	$577,222.46	$46,177.80	$563,295.45
8.	$563,295.45	$45,063.64	$548,254.28
9.	$548,254.28	$43,860.34	$532,009.82
10.	$532,009.82	$42,560.79	$514,465.80
11.	$514,465.80	$41,157.26	$495,518.26
12.	$495,518.26	$39,641.46	$475,054.91
13.	$475,054.91	$38,004.39	$452,954.50
14.	$452,954.50	$36,236.36	$429,086.05
15.	$429,086.05	$34,326.88	$403,308.13
16.	$403,308.13	$32,264.65	$375,467.98
17.	$375,467.98	$30,037.44	$345,400.61
18.	$345,400.61	$27,632.05	$312,927.86
19.	$312,927.86	$25,034.23	$277,857.28
20.	$277,857.28	$22,228.58	$239,981.06
21.	$239,981.06	$19,198.48	$199,074.74
22.	$199,074.74	$15,925.98	$154,895.91
23.	$154,895.91	$12,391.67	$107,182.78
24.	$107,182.78	$8,574.62	$55,652.60
25.	$55,652.60	$4,452.21	$0.00