Question

Your eccentric (and rich uncle) is thrilled that you are pursuing your undergraduate in business administration. For the next 40 years (starting 1 year from now; last payment 40 years from now), he will pay you $2000 every odd year (1st, 3rd, etc.) and $3000 every even year (2nd, 4th, etc.). The relevant discount rate is 5% per year. What is the present value of all the money you will receive from this source over the next 40 years?

Please explain with formulas and step by step.

Answer 1

Calculate the present value of all money received using discount factor of 5%
Year	Cash flow	Discount factor @ 5% (1/((1+r)^n))		Present value (Cash flow*Discount factor)
1	$2,000	0.95238	1/(1.05^1)	$1,904.76
2	$3,000	0.90703	1/(1.05^2)	$2,721.09
3	$2,000	0.86384	1/(1.05^3)	$1,727.68
4	$3,000	0.82270	1/(1.05^4)	$2,468.11
5	$2,000	0.78353	1/(1.05^5)	$1,567.05
6	$3,000	0.74622	1/(1.05^6)	$2,238.65
7	$2,000	0.71068	1/(1.05^7)	$1,421.36
8	$3,000	0.67684	1/(1.05^8)	$2,030.52
9	$2,000	0.64461	1/(1.05^9)	$1,289.22
10	$3,000	0.61391	1/(1.05^10)	$1,841.74
11	$2,000	0.58468	1/(1.05^11)	$1,169.36
12	$3,000	0.55684	1/(1.05^12)	$1,670.51
13	$2,000	0.53032	1/(1.05^13)	$1,060.64
14	$3,000	0.50507	1/(1.05^14)	$1,515.20
15	$2,000	0.48102	1/(1.05^15)	$962.03
16	$3,000	0.45811	1/(1.05^16)	$1,374.33
17	$2,000	0.43630	1/(1.05^17)	$872.59
18	$3,000	0.41552	1/(1.05^18)	$1,246.56
19	$2,000	0.39573	1/(1.05^19)	$791.47
20	$3,000	0.37689	1/(1.05^20)	$1,130.67
21	$2,000	0.35894	1/(1.05^21)	$717.88
22	$3,000	0.34185	1/(1.05^22)	$1,025.55
23	$2,000	0.32557	1/(1.05^23)	$651.14
24	$3,000	0.31007	1/(1.05^24)	$930.20
25	$2,000	0.29530	1/(1.05^25)	$590.61
26	$3,000	0.28124	1/(1.05^26)	$843.72
27	$2,000	0.26785	1/(1.05^27)	$535.70
28	$3,000	0.25509	1/(1.05^28)	$765.28
29	$2,000	0.24295	1/(1.05^29)	$485.89
30	$3,000	0.23138	1/(1.05^30)	$694.13
31	$2,000	0.22036	1/(1.05^31)	$440.72
32	$3,000	0.20987	1/(1.05^32)	$629.60
33	$2,000	0.19987	1/(1.05^33)	$399.75
34	$3,000	0.19035	1/(1.05^34)	$571.06
35	$2,000	0.18129	1/(1.05^35)	$362.58
36	$3,000	0.17266	1/(1.05^36)	$517.97
37	$2,000	0.16444	1/(1.05^37)	$328.87
38	$3,000	0.15661	1/(1.05^38)	$469.82
39	$2,000	0.14915	1/(1.05^39)	$298.30
40	$3,000	0.14205	1/(1.05^40)	$426.14
Present value				$42,688.46
Thus, present value of all money is $42,688.46