年金现值计算公式、系数

年金现值怎么计算呢?年金现值的计算公式为：P=[1-(1+i)的-n次方]/i，其中P是现值因子，i是利率、n是时间，设普通年金1元、利率为i、n期的年金现值，记作(P/A，i，n)。年金现值计算公式中，年金现值系数是最重要的参数。下文将为您详细介绍年金现值的计算公式及系数。

年金现值计算公式

1.普通年金现值公式

式中的分式称作“年金现值系数”，记为(P/A，i，n)，可通过直接查阅“1元年金现值表”求得有关的数值，上式也可写作：P=A(P/A，i，n)

2.递延年金现值公式

或

3.终值公式

式中的分式称作“年金终值系数”，记作为(F/A，i，n)，可通过直接查阅“1元年金终值表”求得有关的数值，上式也可写作：F=A(F/A，i，n)

年金现值系数

n	1%	2%	3%	4%	5%	6%	8%	10%	12%	14%	15%	16%	18%	20%	22%	24%	25%	30%	35%	40%	45%	50%
1	0.99	0.98	0.97	0.961	0.952	0.943	0.925	0.909	0.892	0.877	0.869	0.862	0.847	0.833	0.819	0.806	0.799	0.769	0.74	0.714	0.689	0.666
2	1.97	1.941	1.913	1.886	1.859	1.833	1.783	1.735	1.69	1.646	1.625	1.605	1.565	1.527	1.491	1.456	1.44	1.36	1.289	1.224	1.165	1.111
3	2.94	2.883	2.828	2.775	2.723	2.673	2.577	2.486	2.401	2.321	2.283	2.245	2.174	2.106	2.042	1.981	1.952	1.816	1.695	1.588	1.493	1.407
4	3.901	3.807	3.717	3.629	3.545	3.465	3.312	3.169	3.037	2.913	2.854	2.798	2.69	2.588	2.493	2.404	2.361	2.166	1.996	1.849	1.719	1.604
5	4.853	4.713	4.579	4.451	4.329	4.212	3.992	3.79	3.604	3.433	3.352	3.274	3.127	2.99	2.863	2.745	2.689	2.435	2.219	2.035	1.875	1.736
6	5.795	5.601	5.417	5.242	5.075	4.917	4.622	4.355	4.111	3.888	3.784	3.684	3.497	3.325	3.166	3.02	2.951	2.642	2.385	2.167	1.983	1.824
7	6.728	6.471	6.23	6.002	5.786	5.582	5.206	4.868	4.563	4.288	4.16	4.038	3.811	3.604	3.415	3.242	3.161	2.802	2.507	2.262	2.057	1.882
8	7.651	7.325	7.019	6.732	6.463	6.209	5.746	5.334	4.967	4.638	4.487	4.343	4.077	3.837	3.619	3.421	3.328	2.924	2.598	2.33	2.108	1.921
9	8.566	8.162	7.786	7.435	7.107	6.801	6.246	5.759	5.328	4.946	4.771	4.606	4.303	4.03	3.786	3.565	3.463	3.019	2.665	2.378	2.143	1.947
10	9.471	8.982	8.53	8.11	7.721	7.36	6.71	6.144	5.65	5.216	5.018	4.833	4.494	4.192	3.923	3.681	3.57	3.091	2.715	2.413	2.168	1.965
11	10.367	9.786	9.252	8.76	8.306	7.886	7.138	6.495	5.937	5.452	5.233	5.028	4.656	4.327	4.035	3.775	3.656	3.147	2.751	2.438	2.184	1.976
12	11.255	10.575	9.954	9.385	8.863	8.383	7.536	6.813	6.194	5.66	5.42	5.197	4.793	4.439	4.127	3.851	3.725	3.19	2.779	2.455	2.196	1.984
13	12.133	11.348	10.634	9.985	9.393	8.852	7.903	7.103	6.423	5.842	5.583	5.342	4.909	4.532	4.202	3.912	3.78	3.223	2.799	2.468	2.204	1.989
14	13.003	12.106	11.296	10.563	9.898	9.294	8.244	7.366	6.628	6.002	5.724	5.467	5.008	4.61	4.264	3.961	3.824	3.248	2.814	2.477	2.209	1.993
15	13.865	12.849	11.937	11.118	10.379	9.712	8.559	7.606	6.81	6.142	5.847	5.575	5.091	4.675	4.315	4.001	3.859	3.268	2.825	2.483	2.213	1.995
16	14.717	13.577	12.561	11.652	10.837	10.105	8.851	7.823	6.973	6.265	5.954	5.668	5.162	4.729	4.356	4.033	3.887	3.283	2.833	2.488	2.216	1.996
17	15.562	14.291	13.166	12.165	11.274	10.477	9.121	8.021	7.119	6.372	6.047	5.748	5.222	4.774	4.39	4.059	3.909	3.294	2.839	2.491	2.218	1.997
18	16.398	14.992	13.753	12.659	11.689	10.827	9.371	8.201	7.249	6.467	6.127	5.817	5.273	4.812	4.418	4.079	3.927	3.303	2.844	2.494	2.219	1.998
19	17.226	15.678	14.323	13.133	12.085	11.158	9.603	8.364	7.365	6.55	6.198	5.877	5.316	4.843	4.441	4.096	3.942	3.31	2.847	2.495	2.22	1.999
20	18.045	16.351	14.877	13.59	12.462	11.469	9.818	8.513	7.469	6.623	6.259	5.928	5.352	4.869	4.46	4.11	3.953	3.315	2.85	2.497	2.22	1.999
21	18.856	17.011	15.415	14.029	12.821	11.764	10.016	8.648	7.562	6.686	6.312	5.973	5.383	4.891	4.475	4.121	3.963	3.319	2.851	2.497	2.221	1.999
22	19.66	17.658	15.936	14.451	13.163	12.041	10.2	8.771	7.644	6.742	6.358	6.011	5.409	4.909	4.488	4.129	3.97	3.322	2.853	2.498	2.221	1.999
23	20.455	18.292	16.443	14.856	13.488	12.303	10.371	8.883	7.718	6.792	6.398	6.044	5.432	4.924	4.498	4.137	3.976	3.325	2.854	2.498	2.221	1.999
24	21.243	18.913	16.935	15.246	13.798	12.55	10.528	8.984	7.784	6.835	6.433	6.072	5.45	4.937	4.507	4.142	3.981	3.327	2.855	2.499	2.221	1.999
25	22.023	19.523	17.413	15.622	14.093	12.783	10.674	9.077	7.843	6.872	6.464	6.097	5.466	4.947	4.513	4.147	3.984	3.328	2.855	2.499	2.222	1.999
26	22.795	20.121	17.876	15.982	14.375	13.003	10.809	9.16	7.895	6.906	6.49	6.118	5.48	4.956	4.519	4.151	3.987	3.329	2.855	2.499	2.222	1.999
27	23.559	20.706	18.327	16.329	14.643	13.21	10.935	9.237	7.942	6.935	6.513	6.136	5.491	4.963	4.524	4.154	3.99	3.33	2.856	2.499	2.222	1.999
28	24.316	21.281	18.764	16.663	14.898	13.406	11.051	9.306	7.984	6.96	6.533	6.152	5.501	4.969	4.528	4.156	3.992	3.331	2.856	2.499	2.222	1.999
29	25.065	21.844	19.188	16.983	15.141	13.59	11.158	9.369	8.021	6.983	6.55	6.165	5.509	4.974	4.531	4.158	3.993	3.331	2.856	2.499	2.222	1.999
30	25.807	22.396	19.6	17.292	15.372	13.764	11.257	9.426	8.055	7.002	6.565	6.177	5.516	4.978	4.533	4.16	3.995	3.332	2.856	2.499	2.222	1.999
40	32.834	27.355	23.114	19.792	17.159	15.046	11.924	9.779	8.243	7.105	6.641	6.233	5.548	4.996	4.543	4.165	3.999	3.333	2.857	2.499	2.222	1.999
50	39.196	31.423	25.729	21.482	18.255	15.761	12.233	9.914	8.304	7.132	6.66	6.246	5.554	4.999	4.545	4.166	3.999	3.333	2.857	2.499	2.222	1.999

年金现值计算案例

某企业于年初存入10万元，在年利率为10%，半年复利一次的情况下，到第10年末，该企业能得到多少本利和?

依题意，P=10，r=10%，m=2，n=10

则：i=(1+r/m)m-1= i=(1+10%/2)2-1=10.25%

F=P(1+i)n=10×(1+10.25%)10=26.53(万元)

这种方法的缺点是调整后的实际利率往往带有小数点，不便于查表。可以把利率变为r/m，期数相应变为m×n，则有：

F=P(1+r/m) m×n=10×(1+10%/2)20=10×(F/P,5%,20)=26.53(万元)。