Question

For an individual that starts working at age 25 and continues to age 70, calculate the lump sum savings that the individual will have by age 70 in both nominal and real dollars .Also calculate the level 30 year annuity that the individual could collect until age 100 by annuitizing the lump sum at age 70. Beginning Salary is 85,000.

1. Pick a starting salary at age 25. Pick an average annual salary percent increase to age 50. After age 50 assume the salary grows at the rate of inflation only.

2. Use a constant percent of salary saved each year.

3. Use a constant rate of inflation of 2%.

4. Use a constant annual portfolio return of 6% nominal.

5. Assume no taxes.

Answer 1

		Beginning Salary	$85,000
		Annual increase in Salary till age 50	4%	(Assumed)
		Salary in year (N+1)=1.04 *Salary in Year(N)
		Where N< or =25
		After age 50 annual increase in salary	2%	(Inflation Rate)
		Salary in year (N+1)=1.02 *Salary in Year(N)
		Where N>25
		Percent of salary saved each year	10%	(assumed)
		Number of years of saving =(70-25)	45
		Future value of saving at end of 45 years
		(Saving )*((1+i)^(45-N))
		i=annual return =6%=0.06
		N=Year of saving
		N	A	B=A*10%	FV=B*(1.06^(45-N))
	Age	Year	Salary	Savings	Future Value
	25	1	$85,000	$8,500	$110,377
	26	2	$88,400	$8,840	$108,294
	27	3	$91,936	$9,194	$106,251
	28	4	$95,613	$9,561	$104,246
	29	5	$99,438	$9,944	$102,279
	30	6	$103,415	$10,342	$100,349
	31	7	$107,552	$10,755	$98,456
	32	8	$111,854	$11,185	$96,598
	33	9	$116,328	$11,633	$94,776
	34	10	$120,982	$12,098	$92,987
	35	11	$125,821	$12,582	$91,233
	36	12	$130,854	$13,085	$89,512
	37	13	$136,088	$13,609	$87,823
	38	14	$141,531	$14,153	$86,166
	39	15	$147,192	$14,719	$84,540
	40	16	$153,080	$15,308	$82,945
	41	17	$159,203	$15,920	$81,380
	42	18	$165,572	$16,557	$79,844
	43	19	$172,194	$17,219	$78,338
	44	20	$179,082	$17,908	$76,860
	45	21	$186,245	$18,625	$75,410
	46	22	$193,695	$19,370	$73,987
	47	23	$201,443	$20,144	$72,591
	48	24	$209,501	$20,950	$71,221
	49	25	$217,881	$21,788	$69,877
	50	26	$222,238	$22,224	$67,240
	51	27	$226,683	$22,668	$64,703
	52	28	$231,217	$23,122	$62,261
	53	29	$235,841	$23,584	$59,912
	54	30	$240,558	$24,056	$57,651
	55	31	$245,369	$24,537	$55,476
	56	32	$250,277	$25,028	$53,382
	57	33	$255,282	$25,528	$51,368
	58	34	$260,388	$26,039	$49,429
	59	35	$265,596	$26,560	$47,564