Amount of An Annuity

Amount of An Annuity: ((1 + i)ⁿ-1)/i

If a principal A is invested at the end of each year at interest rate i compounded annually, then at the end of n years the accumulated amount is F = A((1 + i)ⁿ-1)/i. The ((1 + i)ⁿ-1)/i is the compound amount if $1 invested at the end of each year.

How To Use:

You need to find the compound amount of an annuity in which $1000 is invested at the end of each year, after being invested for 5 years at 7½% interest rate p.a.
Find the column with N Years = 5
Find the row 7½%, the number inside the cell is 5.80839
After 5 years, the compound amount would be 1000 × 5.80839 = $5808.39

i %	N Years
	1	2	3	4	5	6	7	8	9	10
1	1.00000	2.01000	3.03010	4.06040	5.10101	6.15202	7.21354	8.28567	9.36853	10.4622
1¼	1.00000	2.01250	3.03766	4.07563	5.12657	6.19065	7.26804	8.35889	9.46337	10.5817
1½	1.00000	2.01500	3.04522	4.09090	5.15227	6.22955	7.32299	8.43284	9.55933	10.7027
1¾	1.00000	2.01750	3.05281	4.10623	5.17809	6.26871	7.37841	8.50753	9.65641	10.8254
2	1.00000	2.02000	3.06040	4.12161	5.20404	6.30812	7.43428	8.58297	9.75463	10.9497
2¼	1.00000	2.02250	3.06801	4.13704	5.23012	6.34780	7.49062	8.65916	9.85399	11.0757
2½	1.00000	2.02500	3.07563	4.15252	5.25633	6.38774	7.54743	8.73612	9.95452	11.2034
2¾	1.00000	2.02750	3.08326	4.16805	5.28267	6.42794	7.60471	8.81384	10.0562	11.3328
3	1.00000	2.03000	3.09090	4.18363	5.30914	6.46841	7.66246	8.89234	10.1591	11.4639
3¼	1.00000	2.03250	3.09856	4.19926	5.33574	6.50915	7.72069	8.97162	10.2632	11.5967
3½	1.00000	2.03500	3.10622	4.21494	5.36247	6.55015	7.77941	9.05169	10.3685	11.7314
3¾	1.00000	2.03750	3.11391	4.23068	5.38933	6.59143	7.83861	9.13255	10.4750	11.8678
	1	2	3	4	5	6	7	8	9	10
4	1.00000	2.04000	3.12160	4.24646	5.41632	6.63298	7.89829	9.21423	10.5828	12.0061
4¼	1.00000	2.04250	3.12931	4.26230	5.44345	6.67480	7.95848	9.29671	10.6918	12.1462
4½	1.00000	2.04500	3.13702	4.27819	5.47071	6.71689	8.01915	9.38001	10.8021	12.2882
4¾	1.00000	2.04750	3.14476	4.29413	5.49810	6.75926	8.08033	9.46414	10.9137	12.4321
5	1.00000	2.05000	3.15250	4.31013	5.52563	6.80191	8.14201	9.54911	11.0266	12.5779
5¼	1.00000	2.05250	3.16026	4.32617	5.55329	6.84484	8.20420	9.63492	11.1407	12.7256
5½	1.00000	2.05500	3.16803	4.34227	5.58109	6.88805	8.26689	9.72157	11.2563	12.8754
5¾	1.00000	2.05750	3.17581	4.35842	5.60902	6.93154	8.33011	9.80909	11.3731	13.0271
6	1.00000	2.06000	3.18360	4.37462	5.63709	6.97532	8.39384	9.89747	11.4913	13.1808
6¼	1.00000	2.06250	3.19141	4.39087	5.66530	7.01938	8.45809	9.98672	11.6109	13.3366
6½	1.00000	2.06500	3.19923	4.40717	5.69364	7.06373	8.52287	10.0769	11.7319	13.4944
6¾	1.00000	2.06750	3.20706	4.42353	5.72212	7.10836	8.58818	10.1679	11.8542	13.6544
	1	2	3	4	5	6	7	8	9	10
7	1.00000	2.07000	3.21490	4.43994	5.75074	7.15329	8.65402	10.2598	11.9780	13.8164
7¼	1.00000	2.07250	3.22276	4.45641	5.77950	7.19851	8.72040	10.3526	12.1032	13.9807
7½	1.00000	2.07500	3.23062	4.47292	5.80839	7.24402	8.78732	10.4464	12.2298	14.1471
7¾	1.00000	2.07750	3.23851	4.48949	5.83743	7.28983	8.85479	10.5410	12.3580	14.3157
8	1.00000	2.08000	3.24640	4.50611	5.86660	7.33593	8.92280	10.6366	12.4876	14.4866
8¼	1.00000	2.08250	3.25431	4.52279	5.89592	7.38233	8.99137	10.7332	12.6186	14.6597
8½	1.00000	2.08500	3.26222	4.53951	5.92537	7.42903	9.06050	10.8306	12.7512	14.8351
8¾	1.00000	2.08750	3.27016	4.55629	5.95497	7.47603	9.13018	10.9291	12.8854	15.0128
9	1.00000	2.09000	3.27810	4.57313	5.98471	7.52333	9.20043	11.0285	13.0210	15.1929
9¼	1.00000	2.09250	3.28606	4.59002	6.01459	7.57094	9.27126	11.1288	13.1583	15.3754
9½	1.00000	2.09500	3.29402	4.60696	6.04462	7.61886	9.34265	11.2302	13.2971	15.5603
9¾	1.00000	2.09750	3.30201	4.62395	6.07479	7.66708	9.41462	11.3325	13.4375	15.7476
10	1.00000	2.10000	3.31000	4.64100	6.10510	7.71561	9.48717	11.4359	13.5795	15.9374

i %	N Years
	11	12	13	14	15	16	17	18	19	20
1	11.5668	12.6825	13.8093	14.9474	16.0969	17.2579	18.4304	19.6147	20.8109	22.0190
1¼	11.7139	12.8604	14.0211	15.1964	16.3863	17.5912	18.8111	20.0462	21.2968	22.5630
1½	11.8633	13.0412	14.2368	15.4504	16.6821	17.9324	19.2014	20.4894	21.7967	23.1237
1¾	12.0148	13.2251	14.4565	15.7095	16.9844	18.2817	19.6016	20.9446	22.3112	23.7016
2	12.1687	13.4121	14.6803	15.9739	17.2934	18.6393	20.0121	21.4123	22.8406	24.2974
2¼	12.3249	13.6022	14.9083	16.2437	17.6092	19.0054	20.4330	21.8928	23.3853	24.9115
2½	12.4835	13.7956	15.1404	16.5190	17.9319	19.3802	20.8647	22.3863	23.9460	25.5447
2¾	12.6444	13.9921	15.3769	16.7998	18.2618	19.7640	21.3075	22.8934	24.5230	26.1974
3	12.8078	14.1920	15.6178	17.0863	18.5989	20.1569	21.7616	23.4144	25.1169	26.8704
3¼	12.9736	14.3953	15.8631	17.3787	18.9435	20.5592	22.2273	23.9497	25.7281	27.5642
3½	13.1420	14.6020	16.1130	17.6770	19.2957	20.9710	22.7050	24.4997	26.3572	28.2797
3¾	13.3129	14.8121	16.3676	17.9814	19.6557	21.3927	23.1950	25.0648	27.0047	29.0174
	11	12	13	14	15	16	17	18	19	20
4	13.4864	15.0258	16.6268	18.2919	20.0236	21.8245	23.6975	25.6454	27.6712	29.7781
4¼	13.6624	15.2431	16.8909	18.6088	20.3997	22.2666	24.2130	26.2420	28.3573	30.5625
4½	13.8412	15.4640	17.1599	18.9321	20.7841	22.7193	24.7417	26.8551	29.0636	31.3714
4¾	14.0226	15.6887	17.4339	19.2620	21.1770	23.1829	25.2840	27.4850	29.7906	32.2056
5	14.2068	15.9171	17.7130	19.5986	21.5786	23.6575	25.8404	28.1324	30.5390	33.0660
5¼	14.3937	16.1494	17.9972	19.9421	21.9891	24.1435	26.4110	28.7976	31.3095	33.9532
5½	14.5835	16.3856	18.2868	20.2926	22.4087	24.6411	26.9964	29.4812	32.1027	34.8683
5¾	14.7761	16.6257	18.5817	20.6502	22.8376	25.1507	27.5969	30.1837	32.9193	35.8121
6	14.9716	16.8699	18.8821	21.0151	23.2760	25.6725	28.2129	30.9057	33.7600	36.7856
6¼	15.1701	17.1182	19.1881	21.3874	23.7241	26.2069	28.8448	31.6476	34.6256	37.7897
6½	15.3716	17.3707	19.4998	21.7673	24.1822	26.7540	29.4930	32.4101	35.5167	38.8253
6¾	15.5760	17.6274	19.8173	22.1549	24.6504	27.3143	30.1580	33.1937	36.4343	39.8936
	11	12	13	14	15	16	17	18	19	20
7	15.7836	17.8885	20.1406	22.5505	25.1290	27.8881	30.8402	33.9990	37.3790	40.9955
7¼	15.9943	18.1539	20.4700	22.9541	25.6183	28.4756	31.5401	34.8267	38.3517	42.1322
7½	16.2081	18.4237	20.8055	23.3659	26.1184	29.0772	32.2580	35.6774	39.3532	43.3047
7¾	16.4252	18.6981	21.1472	23.7861	26.6296	29.6934	32.9946	36.5517	40.3844	44.5142
8	16.6455	18.9771	21.4953	24.2149	27.1521	30.3243	33.7502	37.4502	41.4463	45.7620
8¼	16.8691	19.2608	21.8498	24.6524	27.6863	30.9704	34.5254	38.3738	42.5396	47.0491
8½	17.0961	19.5492	22.2109	25.0989	28.2323	31.6320	35.3207	39.3230	43.6654	48.3770
8¾	17.3265	19.8425	22.5787	25.5544	28.7904	32.3096	36.1366	40.2986	44.8247	49.7469
9	17.5603	20.1407	22.9534	26.0192	29.3609	33.0034	36.9737	41.3013	46.0185	51.1601
9¼	17.7976	20.4439	23.3350	26.4935	29.9441	33.7139	37.8325	42.3320	47.2477	52.6181
9½	18.0385	20.7522	23.7236	26.9774	30.5402	34.4416	38.7135	43.3913	48.5135	54.1222
9¾	18.2830	21.0656	24.1195	27.4712	31.1496	35.1867	39.6174	44.4801	49.8169	55.6740
10	18.5312	21.3843	24.5227	27.9750	31.7725	35.9497	40.5447	45.5992	51.1591	57.2750

i %	N Years
	21	22	23	24	25	26	27	28	29	30
1	23.2392	24.4716	25.7163	26.9735	28.2432	29.5256	30.8209	32.1291	33.4504	34.7849
1¼	23.8450	25.1431	26.4574	27.7881	29.1354	30.4996	31.8809	33.2794	34.6954	36.1291
1½	24.4705	25.8376	27.2251	28.6335	30.0630	31.5140	32.9867	34.4815	35.9987	37.5387
1¾	25.1164	26.5559	28.0207	29.5110	31.0275	32.5704	34.1404	35.7379	37.3633	39.0172
2	25.7833	27.2990	28.8450	30.4219	32.0303	33.6709	35.3443	37.0512	38.7922	40.5681
2¼	26.4720	28.0676	29.6992	31.3674	33.0732	34.8173	36.6007	38.4242	40.2888	42.1953
2½	27.1833	28.8629	30.5844	32.3490	34.1578	36.0117	37.9120	39.8598	41.8563	43.9027
2¾	27.9178	29.6856	31.5019	33.3682	35.2858	37.2562	39.2808	41.3610	43.4984	45.6946
3	28.6765	30.5368	32.4529	34.4265	36.4593	38.5530	40.7096	42.9309	45.2189	47.5754
3¼	29.4601	31.4175	33.4386	35.5254	37.6799	39.9045	42.2014	44.5730	47.0216	49.5498
3½	30.2695	32.3289	34.4604	36.6665	38.9499	41.3131	43.7591	46.2906	48.9108	51.6227
3¾	31.1055	33.2720	35.5197	37.8517	40.2711	42.7813	45.3856	48.0875	50.8908	53.7992
	21	22	23	24	25	26	27	28	29	30
4	31.9692	34.2480	36.6179	39.0826	41.6459	44.3117	47.0842	49.9676	52.9663	56.0849
4¼	32.8614	35.2580	37.7565	40.3611	43.0765	45.9072	48.8583	51.9348	55.1420	58.4855
4½	33.7831	36.3034	38.9370	41.6892	44.5652	47.5706	50.7113	53.9933	57.4230	61.0071
4¾	34.7354	37.3853	40.1611	43.0688	46.1146	49.3050	52.6470	56.1477	59.8147	63.6559
5	35.7193	38.5052	41.4305	44.5020	47.7271	51.1135	54.6691	58.4026	62.3227	66.4388
5¼	36.7358	39.6644	42.7468	45.9910	49.4055	52.9993	56.7818	60.7628	64.9529	69.3629
5½	37.7861	40.8643	44.1118	47.5380	51.1526	54.9660	58.9891	63.2335	67.7114	72.4355
5¾	38.8713	42.1064	45.5275	49.1454	52.9712	57.0171	61.2956	65.8201	70.6047	75.6645
6	39.9927	43.3923	46.9958	50.8156	54.8645	59.1564	63.7058	68.5281	73.6398	79.0582
6¼	41.1515	44.7235	48.5187	52.5511	56.8356	61.3878	66.2245	71.3635	76.8238	82.6253
6½	42.3490	46.1016	50.0982	54.3546	58.8877	63.7154	68.8569	74.3326	80.1642	86.3749
6¾	43.5864	47.5285	51.7366	56.2289	61.0243	66.1435	71.6081	77.4417	83.6690	90.3167
	21	22	23	24	25	26	27	28	29	30
7	44.8652	49.0057	53.4361	58.1767	63.2490	68.6765	74.4838	80.6977	87.3465	94.4608
7¼	46.1867	50.5353	55.1991	60.2010	65.5656	71.3191	77.4897	84.1077	91.2055	98.8179
7½	47.5525	52.1190	57.0279	62.3050	67.9779	74.0762	80.6319	87.6793	95.2553	103.399
7¾	48.9641	53.7588	58.9251	64.4918	70.4899	76.9529	83.9167	91.4203	99.5053	108.217
8	50.4229	55.4568	60.8933	66.7648	73.1059	79.9544	87.3508	95.3388	103.966	113.283
8¼	51.9307	57.2150	62.9352	69.1274	75.8304	83.0864	90.9410	99.4436	108.648	118.611
8½	53.4891	59.0356	65.0537	71.5832	78.6678	86.3546	94.6947	103.744	113.562	124.215
8¾	55.0997	60.9210	67.2516	74.1361	81.6230	89.7650	98.6194	108.249	118.720	130.108
9	56.7645	62.8733	69.5319	76.7898	84.7009	93.3240	102.723	112.968	124.135	136.308
9¼	58.4853	64.8951	71.8980	79.5485	87.9067	97.0381	107.014	117.913	129.820	142.828
9½	60.2638	66.9889	74.3529	82.4164	91.2459	100.914	111.501	123.094	135.788	149.688
9¾	62.1022	69.1572	76.9000	85.3978	94.7241	104.960	116.193	128.522	142.053	156.903
10	64.0025	71.4027	79.5430	88.4973	98.3471	109.182	121.100	134.210	148.631	164.494

i %	N Years
	31	32	33	34	35	36	37	38	39	40
1	36.1327	37.4941	38.8690	40.2577	41.6603	43.0769	44.5076	45.9527	47.4123	48.8864
1¼	37.5807	39.0504	40.5386	42.0453	43.5709	45.1155	46.6794	48.2629	49.8662	51.4896
1½	39.1018	40.6883	42.2986	43.9331	45.5921	47.2760	48.9851	50.7199	52.4807	54.2679
1¾	40.7000	42.4122	44.1544	45.9271	47.7308	49.5661	51.4335	53.3336	55.2670	57.2341
2	42.3794	44.2270	46.1116	48.0338	49.9945	51.9944	54.0343	56.1149	58.2372	60.4020
2¼	44.1447	46.1379	48.1760	50.2600	52.3908	54.5696	56.7974	59.0754	61.4046	63.7862
2½	46.0003	48.1503	50.3540	52.6129	54.9282	57.3014	59.7339	62.2273	64.7830	67.4026
2¾	47.9512	50.2699	52.6523	55.1002	57.6155	60.1999	62.8554	65.5839	68.3875	71.2681
3	50.0027	52.5028	55.0778	57.7302	60.4621	63.2759	66.1742	69.1594	72.2342	75.4013
3¼	52.1602	54.8554	57.6382	60.5114	63.4780	66.5411	69.7037	72.9690	76.3405	79.8216
3½	54.4295	57.3345	60.3412	63.4532	66.6740	70.0076	73.4579	77.0289	80.7249	84.5503
3¾	56.8167	59.9473	63.1954	66.5652	70.0614	73.6887	77.4520	81.3565	85.4073	89.6101
	31	32	33	34	35	36	37	38	39	40
4	59.3283	62.7015	66.2095	69.8579	73.6522	77.5983	81.7022	85.9703	90.4091	95.0255
4¼	61.9712	65.6049	69.3931	73.3424	77.4594	81.7514	86.2259	90.8905	95.7533	100.823
4½	64.7524	68.6662	72.7562	77.0303	81.4966	86.1640	91.0413	96.1382	101.464	107.030
4¾	67.6796	71.8944	76.3094	80.9341	85.7784	90.8529	96.1684	101.736	107.569	113.678
5	70.7608	75.2988	80.0638	85.0670	90.3203	95.8363	101.628	107.710	114.095	120.800
5¼	74.0044	78.8897	84.0314	89.4430	95.1388	101.134	107.443	114.084	121.073	128.430
5½	77.4194	82.6775	88.2248	94.0771	100.251	106.765	113.637	120.887	128.536	136.606
5¾	81.0152	86.6736	92.6573	98.9851	105.677	112.753	120.236	128.150	136.519	145.369
6	84.8017	90.8898	97.3432	104.184	111.435	119.121	127.268	135.904	145.058	154.762
6¼	88.7893	95.3387	102.297	109.691	117.547	125.893	134.762	144.184	154.196	164.833
6½	92.9892	100.034	107.536	115.526	124.035	133.097	142.748	153.027	163.974	175.632
6¾	97.4130	104.988	113.075	121.708	130.923	140.760	151.262	162.472	174.439	187.213
	31	32	33	34	35	36	37	38	39	40
7	102.073	110.218	118.933	128.259	138.237	148.913	160.337	172.561	185.640	199.635
7¼	106.982	115.738	125.130	135.201	146.003	157.589	170.014	183.340	197.632	212.960
7½	112.154	121.566	131.683	142.560	154.252	166.820	180.332	194.857	210.471	227.257
7¾	117.604	127.718	138.616	150.359	163.012	176.645	191.335	207.164	224.219	242.596
8	123.346	134.214	145.951	158.627	172.317	187.102	203.070	220.316	238.941	259.057
8¼	129.397	141.072	153.710	167.391	182.201	198.233	215.587	234.373	254.709	276.722
8½	135.773	148.314	161.920	176.684	192.702	210.081	228.938	249.398	271.597	295.683
8¾	142.493	155.961	170.608	186.536	203.858	222.695	243.181	265.459	289.687	316.035
9	149.575	164.037	179.800	196.982	215.711	236.125	258.376	282.630	309.066	337.882
9¼	157.040	172.566	189.528	208.060	228.305	250.424	274.588	300.987	329.828	361.338
9½	164.908	181.574	199.824	219.807	241.688	265.649	291.886	320.615	352.073	386.520
9¾	173.201	191.088	210.719	232.265	255.910	281.862	310.343	341.602	375.908	413.559
10	181.943	201.138	222.252	245.477	271.024	299.127	330.039	364.043	401.448	442.593

i %	N Years
	41	42	43	44	45	46	47	48	49	50
1	50.3752	51.8790	53.3978	54.9318	56.4811	58.0459	59.6263	61.2226	62.8348	64.4632
1¼	53.1332	54.7973	56.4823	58.1883	59.9157	61.6646	63.4354	65.2284	67.0437	68.8818
1½	56.0819	57.9231	59.7920	61.6889	63.6142	65.5684	67.5519	69.5652	71.6087	73.6828
1¾	59.2357	61.2724	63.3446	65.4532	67.5986	69.7816	72.0027	74.2628	76.5624	78.9022
2	62.6100	64.8622	67.1595	69.5027	71.8927	74.3306	76.8172	79.3535	81.9406	84.5794
2¼	66.2214	68.7113	71.2574	73.8606	76.5225	79.2443	82.0273	84.8729	87.7825	90.7576
2½	70.0876	72.8398	75.6608	78.5523	81.5161	84.5540	87.6679	90.8596	94.1311	97.4843
2¾	74.2280	77.2693	80.3942	83.6050	86.9042	90.2940	93.7771	97.3560	101.033	104.812
3	78.6633	82.0232	85.4839	89.0484	92.7199	96.5015	100.397	104.408	108.541	112.797
3¼	83.4158	87.1268	90.9584	94.9146	98.9993	103.217	107.571	112.067	116.710	121.503
3½	88.5095	92.6074	96.8486	101.238	105.782	110.484	115.351	120.388	125.602	130.998
3¾	93.9705	98.4944	103.188	108.057	113.110	118.351	123.789	129.431	135.285	141.358
	41	42	43	44	45	46	47	48	49	50
4	99.8265	104.820	110.012	115.413	121.029	126.871	132.945	139.263	145.834	152.667
4¼	106.108	111.617	117.361	123.349	129.591	136.099	142.883	149.956	157.329	165.015
4½	112.847	118.925	125.276	131.914	138.850	146.098	153.673	161.588	169.859	178.503
4¾	120.078	126.782	133.804	141.160	148.865	156.936	165.390	174.246	183.523	193.240
5	127.840	135.232	142.993	151.143	159.700	168.685	178.119	188.025	198.427	209.348
5¼	136.172	144.321	152.898	161.925	171.426	181.426	191.951	203.028	214.687	226.959
5½	145.119	154.100	163.576	173.573	184.119	195.246	206.984	219.368	232.434	246.217
5¾	154.727	164.624	175.090	186.158	197.862	210.239	223.327	237.169	251.806	267.285
6	165.048	175.951	187.508	199.758	212.744	226.508	241.099	256.565	272.958	290.336
6¼	176.135	188.143	200.902	214.459	228.862	244.166	260.427	277.703	296.060	315.564
6½	188.048	201.271	215.354	230.352	246.325	263.336	281.453	300.747	321.295	343.180
6¾	200.850	215.407	230.947	247.536	265.245	284.149	304.329	325.871	348.868	373.416
	41	42	43	44	45	46	47	48	49	50
7	214.610	230.632	247.776	266.121	285.749	306.752	329.224	353.270	378.999	406.529
7¼	229.400	247.032	265.941	286.222	307.973	331.301	356.321	383.154	411.932	442.798
7½	245.301	264.698	285.551	307.967	332.065	357.969	385.817	415.753	447.935	482.530
7¾	262.397	283.733	306.722	331.493	358.184	386.943	417.931	451.321	487.298	526.064
8	280.781	304.244	329.583	356.950	386.506	418.426	452.900	490.132	530.343	573.770
8¼	300.552	326.347	354.271	384.498	417.219	452.640	490.983	532.489	577.419	626.056
8½	321.816	350.170	380.934	414.314	450.530	489.825	532.461	578.720	628.911	683.368
8¾	344.688	375.848	409.735	446.586	486.663	530.246	577.642	629.186	685.240	746.198
9	369.292	403.528	440.846	481.522	525.859	574.186	626.863	684.280	746.866	815.084
9¼	395.761	433.369	474.456	519.343	568.382	621.958	680.489	744.434	814.294	890.616
9½	424.239	465.542	510.769	560.292	614.519	673.899	738.919	810.116	888.077	973.445
9¾	454.881	500.232	550.004	604.630	664.581	730.378	802.590	881.842	968.822	1064.28
10	487.852	537.637	592.401	652.641	718.905	791.795	871.975	960.172	1057.19	1163.91

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