Question

In trying to apply my knowledge in the real world, I am trying to create a realistic retirement schedule. However, I am running into difficulties using both a financial calculator as well as our equations from class in doing this.

I am trying to do the following: plan a retirement schedule between the ages of 25 and 70, in which I would deposit 20% of my income each year. The income starts at 80,000 with an annual growth rate of 4% and, to be realistic, assuming an interest rate of 2.5%. I will assume for simplicity that I receive my first salary ($80,000) when I turn 25, and my last salary when I turn 70. As soon as I receive a salary, I will save 20% of it.

I would like to know (1) how much I will have in my retirement account when I turn 70, immediately after the last deposit, and (2) what single deposit made on my 25^th birthday would give the same account balance when I turn 70.

However, this raises issues, as if I try to use the equation for the present value of a growing annuity with a 4% growth rate and 2.5% discount rate, r-g will yield a negative number. Also, I could not find online how to do this on my HP 10bII+ financial calculator and I don't want to manually enter 46 payments.

Do you know how I could overcome this obstacle?

All the best,

Jimmy

Unfortunately, I forgot to reply Jimmy’s email and I would like to get back to him as soon as possible. I want to answer Jimmy’s questions using the formulas we learned in class (not the calculator or Excel). You may use the calculator or Excel for calculations, but I want to send Jimmy the formula solution. Can you help me draft a response?

1. (3 points) Start by drawing the timeline, showing the first three and the last two deposits, ie the deposits at t = 25, 26, 27, 69 and 70 (the amount of each deposit and how you calculated it).
2. (3 points) Briefly comment on Jimmy’s concern that “if I try to use the equation for the present value of a growing annuity with a 4% growth rate and 2.5% discount rate, r-g will yield a negative number”. (3 sentences at most)
3. (5 points) How much will Jimmy have in his retirement account when he turns 70, immediately after the last deposit?
4. (5 points) What single deposit made on Jimmy’s 25^th birthday would give the same account balance when he turns 70?

Answer 1

Year of Deposit	Annual Salary	Deposit (20%)	(1+r)	Period (n)	(1+r)^n	Value of each deposit At 70 =Deposit * (1+r)^n
25	80,000	16,000	1.025	45	3.0379	48,606
26	83,200	16,640	1.025	44	2.9638	49,318
27	86,528	17,306	1.025	43	2.8915	50,039
28	89,989	17,998	1.025	42	2.8210	50,772
29	93,589	18,718	1.025	41	2.7522	51,515
30	97,332	19,466	1.025	40	2.6851	52,269
31	1,01,226	20,245	1.025	39	2.6196	53,034
32	1,05,275	21,055	1.025	38	2.5557	53,810
33	1,09,486	21,897	1.025	37	2.4933	54,597
34	1,13,865	22,773	1.025	36	2.4325	55,396
35	1,18,420	23,684	1.025	35	2.3732	56,207
36	1,23,156	24,631	1.025	34	2.3153	57,029
37	1,28,083	25,617	1.025	33	2.2589	57,864
38	1,33,206	26,641	1.025	32	2.2038	58,711
39	1,38,534	27,707	1.025	31	2.1500	59,570
40	1,44,075	28,815	1.025	30	2.0976	60,442
41	1,49,838	29,968	1.025	29	2.0464	61,326
42	1,55,832	31,166	1.025	28	1.9965	62,224
43	1,62,065	32,413	1.025	27	1.9478	63,134
44	1,68,548	33,710	1.025	26	1.9003	64,058
45	1,75,290	35,058	1.025	25	1.8539	64,996
46	1,82,301	36,460	1.025	24	1.8087	65,947
47	1,89,594	37,919	1.025	23	1.7646	66,912
48	1,97,177	39,435	1.025	22	1.7216	67,891
49	2,05,064	41,013	1.025	21	1.6796	68,884
50	2,13,267	42,653	1.025	20	1.6386	69,893
51	2,21,798	44,360	1.025	19	1.5987	70,915
52	2,30,669	46,134	1.025	18	1.5597	71,953
53	2,39,896	47,979	1.025	17	1.5216	73,006
54	2,49,492	49,898	1.025	16	1.4845	74,074
55	2,59,472	51,894	1.025	15	1.4483	75,159
56	2,69,851	53,970	1.025	14	1.4130	76,258
57	2,80,645	56,129	1.025	13	1.3785	77,374
58	2,91,870	58,374	1.025	12	1.3449	78,507
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