Question

Assume that a donor offers a choice of contributions (a, b, or c) to a not for profit organization. The organization may select only one of the choices.

Which choice should the organization make to maximize its funds? Why?

Choice (a) the donor will contribute $2,000 on the day after the donation is accepted to an account of the not for profit organization. The donor will similarly contribute $2,000 for each of the next nine anniversary dates of the original donation (10 contributions of $2,000 in all). The organization may invest the funds but may not use or withdrawal any amounts for thirty (30) years from the initial contribution;

Choice (b) the donor will contribute $5,000 per year for twenty years beginning on the eleventh anniversary of the institution’s choice of contributions. The institution may not withdraw or use any funds until the thirtieth anniversary of the contribution choice;

Choice (c) the organization may choose to have $14,000 deposited today in its accounts for investment but may not withdraw or use the funds until thirty years have passed.

Assume prevailing interest returns on US Treasury bonds for the next thirty years will average 4.5%.

Answer 1

Option B should the organization make to maximize its fund. Because it fund value at end of 30 year is higher compare to other options.

Interest income = Beginning Fund * 4.5%

Ending Fund = Beginning Fund + interest income +Contribution in fund

Options A
The donor will contribute $2,000 on the day after the donation is accepted to an account of the not for profit organization. The donor will similarly contribute $2,000 for each of the next nine anniversary dates of the original donation (10 contributions of $2,000 in all). The organization may invest the funds but may not use or withdrawal any amounts for thirty (30) years from the initial contribution
Year	Beginning Fund	Interest income	Contribution in fund	Ending Fund
0			2000.00	2000.00
1	2000.00	90.00	2000.00	4090.00
2	4090.00	184.05	2000.00	6274.05
3	6274.05	282.33	2000.00	8556.38
4	8556.38	385.04	2000.00	10941.42
5	10941.42	492.36	2000.00	13433.78
6	13433.78	604.52	2000.00	16038.30
7	16038.30	721.72	2000.00	18760.03
8	18760.03	844.20	2000.00	21604.23
9	21604.23	972.19	2000.00	24576.42
10	24576.42	1105.94		25682.36
11	25682.36	1155.71		26838.06
12	26838.06	1207.71		28045.78
13	28045.78	1262.06		29307.84
14	29307.84	1318.85		30626.69
15	30626.69	1378.20		32004.89
16	32004.89	1440.22		33445.11
17	33445.11	1505.03		34950.14
18	34950.14	1572.76		36522.90
19	36522.90	1643.53		38166.43
20	38166.43	1717.49		39883.92
21	39883.92	1794.78		41678.69
22	41678.69	1875.54		43554.23
23	43554.23	1959.94		45514.17
24	45514.17	2048.14		47562.31
25	47562.31	2140.30		49702.62
26	49702.62	2236.62		51939.23
27	51939.23	2337.27		54276.50
28	54276.50	2442.44		56718.94
29	56718.94	2552.35		59271.29
30	59271.29	2667.21		61938.50

Options B
The donor will contribute $5,000 per year for twenty years beginning on the eleventh anniversary of the institution’s choice of contributions. The institution may not withdraw or use any funds until the thirtieth anniversary of the contribution choice; (contribution made at beginning of 11 year. It means interest revenue arise for 11th year also. So we can consider under contribution in year 10.)
Year	Beginning Fund	Interest income	Contribution in fund	Ending Fund
0				0.00
1	0.00	0.00		0.00
2	0.00	0.00		0.00
3	0.00	0.00		0.00
4	0.00	0.00		0.00
5	0.00	0.00		0.00
6	0.00	0.00		0.00
7	0.00	0.00		0.00
8	0.00	0.00		0.00
9	0.00	0.00		0.00
10	0.00	0.00	5000.00	5000.00
11	5000.00	225.00	5000.00	10225.00
12	10225.00	460.13	5000.00	15685.13
13	15685.13	705.83	5000.00	21390.96
14	21390.96	962.59	5000.00	27353.55
15	27353.55	1230.91	5000.00	33584.46
16	33584.46	1511.30	5000.00	40095.76
17	40095.76	1804.31	5000.00	46900.07
18	46900.07	2110.50	5000.00	54010.57
19	54010.57	2430.48	5000.00	61441.05
20	61441.05	2764.85	5000.00	69205.89
21	69205.89	3114.27	5000.00	77320.16
22	77320.16	3479.41	5000.00	85799.57
23	85799.57	3860.98	5000.00	94660.55
24	94660.55	4259.72	5000.00	103920.27
25	103920.27	4676.41	5000.00	113596.68
26	113596.68	5111.85	5000.00	123708.53
27	123708.53	5566.88	5000.00	134275.42
28	134275.42	6042.39	5000.00	145317.81
29	145317.81	6539.30	5000.00	156857.11
30	156857.11	7058.57		163915.68

Options C
The organization may choose to have $14,000 deposited today in its accounts for investment but may not withdraw or use the funds until thirty years have passed.
Year	Beginning Fund	Interest income	Contribution in fund	Ending Fund
0			14000.00	14000.00
1	14000.00	630.00		14630.00
2	14630.00	658.35		15288.35
3	15288.35	687.98		15976.33
4	15976.33	718.93		16695.26
5	16695.26	751.29		17446.55
6	17446.55	785.09		18231.64
7	18231.64	820.42		19052.07
8	19052.07	857.34		19909.41
9	19909.41	895.92		20805.33
10	20805.33	936.24		21741.57
11	21741.57	978.37		22719.94
12	22719.94	1022.40		23742.34
13	23742.34	1068.41		24810.75
14	24810.75	1116.48		25927.23
15	25927.23	1166.73		27093.95
16	27093.95	1219.23		28313.18
17	28313.18	1274.09		29587.28
18	29587.28	1331.43		30918.70
19	30918.70	1391.34		32310.04
20	32310.04	1453.95		33764.00
21	33764.00	1519.38		35283.38
22	35283.38	1587.75		36871.13
23	36871.13	1659.20		38530.33
24	38530.33	1733.86		40264.19
25	40264.19	1811.89		42076.08
26	42076.08	1893.42		43969.51
27	43969.51	1978.63		45948.13
28	45948.13	2067.67		48015.80
29	48015.80	2160.71		50176.51
30	50176.51	2257.94		52434.45