Suppose that your rich uncle has $1,000,000 that he wishes to distribute to his heirs at the rate of $100,000 per year. If the $1,000,000 is deposited in a bank account that earns 6% interest per year, how many years will it take to completely deplete the account? How long will it take if the

Question

Suppose that your rich uncle has $1,000,000 that he wishes to distribute to his heirs at the rate of $100,000 per year. If the $1,000,000 is deposited in a bank account that earns 6% interest per year, how many years will it take to completely deplete the account? How long will it take if the account earns 8% interest per year instead of 6%? (4.7)

Accepted Answer

$100,000 = $1,000,000 (A/P, 6%, N), so (A/P, 6%, N) = 0.10.
From Table C-9, 15≤ N ≤ 16. If i = 8%, Table C-11 gives us 20 ≤ N ≤ 21.

Table C-9Discrete Compounding; i = 6%
Single Payment				Uniform Series				Uniform Gradient
Compound Amount Factor		Present Worth Factor		Compound Amount Factor	Present Worth Factor	Sinking Fund Factor	Capital Recovery Factor	Gradient Present Worth Factor		Gradient Uniform Series Factor
N	To Find F given P F/P		To Find P Given F P/F	To Find F Given A F/A	To Find P Given A P/A	To Find A Given F A/F	To Find A Given P A/P	To Find P Given G P/G	To Find A given G A/G	N
1	1.0600		0.9434	1.0000	0.9434	1.0000	1.0600	0.000	0.0000	1
2	1.1236		0.8900	2.0600	1.8334	0.4854	0.5454	0.890	0.4854	2
3	1.1910		0.8396	3.1836	2.6730	0.3141	0.3741	2.569	0.9612	3
4	1.2625		0.7921	4.3746	3.4651	0.2286	0.2886	4.946	1.4272	4
5	1.3382		0.7473	5.6371	4.2124	0.1774	0.2374	7.935	1.8836	5
6	1.4185		0.7050	6.9753	4.9173	0.1434	0.2034	11.459	2.3304	6
7	1.5036		0.6651	8.3938	5.5824	0.1191	0.1791	15.450	2.7676	7
8	1.5938		0.6274	9.8975	6.2098	0.1010	0.1610	19.842	3.1952	8
9	1.6895		0.5919	11.4913	6.8017	0.0870	0.1470	24.577	3.6133	9
10	1.7908		0.5584	13.1808	7.3601	0.0759	0.1359	29.602	4.0220	10
11	1.8983		0.5268	14.9716	7.8869	0.0668	0.1268	34.870	4.4213	11
12	2.0122		0.4970	16.8699	8.3838	0.0593	0.1193	40.337	4.8113	12
13	2.1329		0.4688	18.8821	8.8527	0.0530	0.1130	45.963	5.1920	13
14	2.2609		0.4423	21.0151	9.2950	0.0476	0.1076	51.713	5.5635	14
15	2.3966		0.4173	23.2760	9.7122	0.0430	0.1030	57.555	5.9260	15
16	2.5404		0.3936	25.6725	10.1059	0.0390	0.0990	63.459	6.2794	16
17	2.6928		0.3714	28.2129	10.4773	0.0354	0.0954	69.401	6.6240	17
18	2.8543		0.3503	30.9057	10.8276	0.0324	0.0924	75.357	6.9597	18
19	3.0256		0.3305	33.7600	11.1581	0.0296	0.0896	81.306	7.2867	19
20	3.2071		0.3118	36.7856	11.4699	0.0272	0.0872	87.230	7.6051	20
21	3.3996		0.2942	39.9927	11.7641	0.0250	0.0850	93.114	7.9151	21
22	3.6035		0.2775	43.3923	12.0416	0.0230	0.0830	98.941	8.2166	22
23	3.8197		0.2618	46.9958	12.3034	0.0213	0.0813	104.701	8.5099	23
24	4.0489		0.2470	50.8156	12.5504	0.0197	0.0797	110.381	8.7951	24
25	4.2919		0.2330	54.8645	12.7834	0.0182	0.0782	115.973	9.0722	25
30	5.7435		0.1741	79.0582	13.7648	0.0126	0.0726	142.359	10.3422	30
35	7.6861		0.1301	111.4348	14.4982	0.0090	0.0690	165.743	11.4319	35
40	10.2857		0.0972	154.7620	15.0463	0.0065	0.0665	185.957	12.3590	40
45	13.7646		0.0727	212.7435	15.4558	0.0047	0.0647	203.110	13.1413	45
50	18.4202		0.0543	290.3359	15.7619	0.0034	0.0634	217.457	13.7964	50
60	32.9877		0.0303	533.1282	16.1614	0.0019	0.0619	239.043	14.7909	60
80	105.7960		0.0095	1746.5999	16.5091	0.0006	0.0606	262.549	15.9033	80
100	339.3021		0.0029	5638.3681	16.6175	0.0002	0.0602	272.047	16.3711	100
∞					16.6667		0.0600			∞

Table C-11 Discrete Compounding; i = 8%
Single Payment				Uniform Series				Uniform Gradient
Compound		Present		Compound	Present	Sinking	Capital	Gradient		Gradient
Amount		Worth		Amount	Worth	Fund	Recovery	Present Worth		Uniform Series
Factor		Factor		Factor	Factor	Factor	Factor	Factor		Factor
N	To Find F		To Find P	To Find F	To Find P	To Find A	To Find A	To Find P	To Find A given G A/G	N
	given P		Given F	Given A	Given A	Given F	Given P	Given G
	F/P		P/F	F/A	P/A	A/F	A/P	P/G
1	1.08		0.9259	1	0.9259	1	1.08	0	0	1
2	1.1664		0.8573	2.08	1.7833	0.4808	0.5608	0.857	0.4808	2
3	1.2597		0.7938	3.2464	2.5771	0.308	0.388	2.445	0.9487	3
4	1.3605		0.735	4.5061	3.3121	0.2219	0.3019	4.65	1.404	4
5	1.4693		0.6806	5.8666	3.9927	0.1705	0.2505	7.372	1.8465	5
6	1.5869		0.6302	7.3359	4.6229	0.1363	0.2163	10.523	2.2763	6
7	1.7138		0.5835	8.9228	5.2064	0.1121	0.1921	14.024	2.6937	7
8	1.8509		0.5403	10.6366	5.7466	0.94	0.174	17.806	3.0985	8
9	1.999		0.5002	12.4876	6.2469	0.0801	0.1601	21.808	3.491	9
10	2.1589		0.4632	14.4866	6.7101	0.069	0.149	25.977	3.8713	10
11	2.3316		0.4289	16.6455	7.139	0.0601	0.1401	30.266	4.2395	11
12	2.5182		0.3971	18.9771	7.5361	0.0527	0.1327	34.634	4.5957	12
13	2.7196		0.3677	21.4953	7.9038	0.0465	0.1265	39.046	4.9402	13
14	2.9372		0.3405	24.2149	8.2442	0.0413	0.1213	43.472	5.2731	14
15	3.1722		0.3152	27.1521	8.5595	0.0368	0.1168	47.886	5.5945	15
16	3.4259		0.2919	30.3243	8.8514	0.033	0.113	52.264	5.9046	16
17	3.7		0.2703	33.7502	9.1216	0.0296	0.1096	56.588	6.2037	17
18	3.996		0.2502	37.4502	9.3719	0.0267	0.1067	60.843	6.492	18
19	4.3157		0.2317	41.4463	9.6036	0.0241	0.1041	65.013	6.7697	19
20	4.661		0.2145	45.762	9.8181	0.0219	0.1041	69.09	7.0369	20
21	5.0338		0.1987	50.4229	10.0168	0.0198	0.0998	73.063	7.294	21
22	5.4365		0.1839	55.4568	10.2007	0.018	0.098	76.926	7.5412	22
23	5.8715		0.1703	60.8933	10.3711	0.0164	0.0964	80.673	7.7786	23
24	6.3412		0.1577	66.8933	10.5288	0.015	0.095	84.3	8.0066	24
25	6.8485		0.146	73.1059	10.6748	0.0137	0.0937	87.804	8.2254	25
30	10.0627		0.0994	113.2832	11.2578	0.0088	0.0888	103.456	9.1897	30
35	14.7853		0.0676	172.3168	11.6546	0.0058	0.0858	116.092	9.9611	35
40	21.7245		0.046	259.0565	11.9246	0.0039	0.0839	126.042	10.5699	40
45	31.9204		0.03123	386.5056	12.1084	0.0026	0.0826	133.733	11.0447	45
50	46.9016		0.0213	573.7702	12.2335	0.0017	0.0817	139.593	11.4107	50
60	101.2571		0.0099	1253.2133	12.3766	0.0008	0.0808	147.3	11.9015	60
80	471.9548		0.0021	5886.9354	12.4735	0.0002	0.0802	155.611	12.3301	80
100	2199.7613		0.0005	27484.516	12.4943	a	0.08	272.047	12.4545	100
∞					12.5		0.08			∞
a Less than 0.0001.

Question 4.H.H: Suppose that your rich uncle has $1,000,000 that he wishes t...

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