Question

1. A worker has the following savings plan: save $50 in month 1, $60 in month 2, $70 in month 3, and so on for five years at 6% annual return, however the compounding is monthly. a. Determine the future value after five years of saving. 10 pts b. Determine the present value after five years of saving. 10 pts

Answer 1

Below are the givens of question :-

1. Savings of month 1 is $50, month 2 is $60, month 3 is $70 and so on for 5 years
2. Rate of interest is 6% per annum or 0.06 in decimal
3. Compounding is monthly

Answer – a

The future value of savings after five years can be calculated by compounding each month investment made by the worker at 6% per annum.

The monthly rate of interest is 0.5% or 0.005 in decimal since compounding is monthly

Computation of Future value of monthly savings

Month	Opening Investment (A)	Invested in Month (B)	Interest [(A+B)*0.005] ( C )	Closing Investment (A+B+C)
1	-	50.00	0.25	50.25
2	50.25	60.00	0.55	110.80
3	110.80	70.00	0.90	181.71
4	181.71	80.00	1.31	263.01
5	263.01	90.00	1.77	354.78
6	354.78	100.00	2.27	457.05
7	457.05	110.00	2.84	569.89
8	569.89	120.00	3.45	693.34
9	693.34	130.00	4.12	827.45
10	827.45	140.00	4.84	972.29
11	972.29	150.00	5.61	1,127.90
12	1,127.90	160.00	6.44	1,294.34
13	1,294.34	170.00	7.32	1,471.66
14	1,471.66	180.00	8.26	1,659.92
15	1,659.92	190.00	9.25	1,859.17
16	1,859.17	200.00	10.30	2,069.47
17	2,069.47	210.00	11.40	2,290.87
18	2,290.87	220.00	12.55	2,523.42
19	2,523.42	230.00	13.77	2,767.19
20	2,767.19	240.00	15.04	3,022.22
21	3,022.22	250.00	16.36	3,288.58
22	3,288.58	260.00	17.74	3,566.33
23	3,566.33	270.00	19.18	3,855.51
24	3,855.51	280.00	20.68	4,156.19
25	4,156.19	290.00	22.23	4,468.42
26	4,468.42	300.00	23.84	4,792.26
27	4,792.26	310.00	25.51	5,127.77
28	5,127.77	320.00	27.24	5,475.01
29	5,475.01	330.00	29.03	5,834.03
30	5,834.03	340.00	30.87	6,204.90
31	6,204.90	350.00	32.77	6,587.68
32	6,587.68	360.00	34.74	6,982.42
33	6,982.42	370.00	36.76	7,389.18
34	7,389.18	380.00	38.85	7,808.03
35	7,808.03	390.00	40.99	8,239.02
36	8,239.02	400.00	43.20	8,682.21
37	8,682.21	410.00	45.46	9,137.67
38	9,137.67	420.00	47.79	9,605.46
39	9,605.46	430.00	50.18	10,085.64
40	10,085.64	440.00	52.63	10,578.27
41	10,578.27	450.00	55.14	11,083.41
42	11,083.41	460.00	57.72	11,601.12
43	11,601.12	470.00	60.36	12,131.48
44	12,131.48	480.00	63.06	12,674.54
45	12,674.54	490.00	65.82	13,230.36
46	13,230.36	500.00	68.65	13,799.01
47	13,799.01	510.00	71.55	14,380.56
48	14,380.56	520.00	74.50	14,975.06
49	14,975.06	530.00	77.53	15,582.58
50	15,582.58	540.00	80.61	16,203.20
51	16,203.20	550.00	83.77	16,836.96
52	16,836.96	560.00	86.98	17,483.95
53	17,483.95	570.00	90.27	18,144.22
54	18,144.22	580.00	93.62	18,817.84
55	18,817.84	590.00	97.04	19,504.88
56	19,504.88	600.00	100.52	20,205.40
57	20,205.40	610.00	104.08	20,919.48
58	20,919.48	620.00	107.70	21,647.18
59	21,647.18	630.00	111.39	22,388.56
60	22,388.56	640.00	115.14	23,143.71

Hence the future value of savings after five years is $23,143.71

Answer – b

Present value (PV) of savings after five years can be calculated by discounting it with the present value (PV) factor

PV of savings after five years = Future value of savings after five years * PV factor

Future value of savings after five years is $23,143.71 calculated above

PV factor is calculated on monthly rate of interest of 0.5% for 60 months

PV factor = 1/(1 + 0.005)↑60

                = 0.74137

On putting these two figures in the above formula, we get –

PV of savings after five years = $23,143.71 * 0.74137

                                                = $ 17,158.10