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Annuity calculator (growth and payout)

Calculate an annuity's future value from regular payments, the payout a lump sum buys over N years, or how long it lasts at a set withdrawal.

更新于 已验证的示例：8

$
$
%
Nominal yearly rate, compounded once per payment period
试一试
Future value
$
Future value: $205,516.83
小数位数：2；取最近值，等距时取偶数末位
Number of payments
240
Present value of the payments
$75,762.66
Total of all payments
$120,000.00
Interest earned
$85,516.83
Rate per period
0.4167%

240 payments of $500.00 grow to $205,516.83 at 5% a year: $120,000.00 paid in and $85,516.83 of interest.

Balance: payments and interest

$0$50K$100K$150K$200K05101520Years
Paid inInterest

Future value

$205.5Kfuture value
Paid in58.4%利息41.6%
Accumulation schedule 行数：20
年Start balancePaid in利息End balance
1$0.00$6,000.00$139.43$6,139.43
2$6,139.43$6,000.00$453.53$12,592.96
3$12,592.96$6,000.00$783.71$19,376.67
4$19,376.67$6,000.00$1,130.77$26,507.44
5$26,507.44$6,000.00$1,495.60$34,003.04
6$34,003.04$6,000.00$1,879.09$41,882.13
7$41,882.13$6,000.00$2,282.20$50,164.33
8$50,164.33$6,000.00$2,705.93$58,870.26
9$58,870.26$6,000.00$3,151.34$68,021.60
10$68,021.60$6,000.00$3,619.54$77,641.14
计算方法 S

  1. Rate per period

    i=0.0512=0.004166666667i = \frac{0.05}{12} = 0.004166666667

  2. Number of payments

    n=240n = 240

  3. Future value of the payments

    500.00×(1+0.004166666667)240−10.004166666667=205,516.83500.00 \times \frac{(1 + 0.004166666667)^{240} - 1}{0.004166666667} = 205{,}516.83

  4. Future value

    FV=205,516.83FV = 205{,}516.83

  5. Present value today

    PV=205,516.83(1+0.004166666667)240=75,762.66PV = \frac{205{,}516.83}{(1 + 0.004166666667)^{240}} = 75{,}762.66

关于Annuity calculator (growth and payout)

An annuity is a series of equal payments at a fixed interest rate. Saving into one, the future value is the payment times ((1 + i)^n − 1) ÷ i, where i is the rate per period and n the number of payments; paying out of one, the payment a lump sum supports is the lump sum times i ÷ (1 − (1 + i)^−n). Payments at the start of each period (an annuity due) earn one extra period of interest. A third mode solves for n, how long a lump sum lasts.

With the defaults, 500 at the end of each month for 20 years at 5% grows to 205,516.83 from 120,000 of payments. Paid out instead, 500,000 at 5% supports 3,299.78 a month for 20 years, and 3,000 a month lasts 23.76 years: 285 full withdrawals and a final 427.00.

The rate is a nominal yearly rate divided by the number of payments a year. Insurance annuity fees, surrender charges, taxes and inflation are not included.

计算示例

Future value of 1,000 a year for 10 years at 5%

我要计算
Future value of regular payments
Payment each period
1000
Starting balance
0
Term
10
Term in
年
Interest rate (per year)
5%
Payments every
年
Payments made at
End (ordinary)
Future value
12,577.89
Total of all payments
10,000.00
Interest earned
2,577.89

核验来源：Future value annuity factor table, 5% and 10 periods: 12.5779; Python decimal 12,577.8925355…

Same payments as an annuity due

我要计算
Future value of regular payments
Payment each period
1000
Starting balance
0
Term
10
Term in
年
Interest rate (per year)
5%
Payments every
年
Payments made at
Start (annuity due)
Future value
13,206.79

核验来源：12,577.89 × 1.05 (annuity-due factor); Python decimal 13,206.7871623…

Excel FV example: 500 now plus 200 at the start of each month, 6%, 10 months

我要计算
Future value of regular payments
Payment each period
200
Starting balance
500
Term
10
Term in
月
Interest rate (per year)
6%
Payments every
月
Payments made at
Start (annuity due)
Future value
2,581.40

核验来源：Microsoft FV documentation: =FV(0.06/12, 10, -200, -500, 1) returns $2,581.40

Excel PV example reversed: 59,777.15 paid out monthly for 20 years at 8%

我要计算
Payout from a lump sum over a set time
Lump sum at the start
59,777.15
Term
20
Term in
年
Interest rate (per year)
8%
Payments every
月
Payments made at
End (ordinary)
Payment each period
500.00

核验来源：Microsoft PV documentation: =PV(0.08/12, 12*20, 500, , 0) returns ($59,777.15)

常见问题

How do you calculate the future value of an annuity?

Multiply the payment by ((1 + i)^n − 1) ÷ i, where i is the rate per period and n the number of payments. 1,000 at the end of each year for 10 years at 5% grows to 1,000 × 12.5779 = 12,577.89; paid at the start of each year (an annuity due) it grows to 13,206.79, 5% more, because every payment earns one more year.

How much does an annuity pay per month?

Divide the lump sum by the present-value factor (1 − (1 + i)^−n) ÷ i. 500,000 at 5% a year (0.4167% a month) paid over 20 years gives 3,299.78 a month, 791,946.89 in total. Microsoft's PV documentation gives the reverse: 500 a month for 20 years at 8% costs 59,777.15 today.

How long will a lump sum last with monthly withdrawals?

Solve n = −ln(1 − P·i ÷ W) ÷ ln(1 + i), with P the lump sum, i the monthly rate and W the withdrawal. 100,000 at 6% with 1,000 taken at the end of each month lasts 138.98 months: 138 full payments and a final 975.78, about 11.6 years. If W is no more than P·i (500 here), the balance never runs out.

What is the difference between an ordinary annuity and an annuity due?

An ordinary annuity pays at the end of each period, like loan repayments; an annuity due pays at the start, like rent. An annuity due is worth (1 + i) times the ordinary one, both in future value and in present value. At 5% a year, a 10-year annuity due of 1,000 accumulates 13,206.79 against 12,577.89.

“Annuity calculator (growth and payout)”有多准确？

准确性取决于输入值和方法的假设。十进制运算使用50位有效数字，但估算、数值方法和源数据的精度可能较低；显示时的舍入并不能消除这些限制。 已按独立来源核验的计算示例：8。 例如，“Future value of 1,000 a year for 10 years at 5%”根据Future value annuity factor table, 5% and 10 periods: 12.5779; Python decimal 12,577.8925355…进行核验。

这种方法出自哪里？

Microsoft Excel FV, PV, PMT and NPER functions (type 0 = end, 1 = start of period); Kellison, The Theory of Interest, 3rd ed., ch. 3 (annuities-immediate and annuities-due).

关于此计算器

FV=S(1+i)n+P (1+i)n−1i(1+i)δ,P=PV i(1−(1+i)−n)(1+i)δ,n=−ln⁡ ⁣(1−PV iW(1+i)δ)ln⁡(1+i)FV = S(1+i)^n + P\,\frac{(1+i)^n-1}{i}(1+i)^{\delta},\qquad P = \frac{PV\,i}{\big(1-(1+i)^{-n}\big)(1+i)^{\delta}},\qquad n = -\frac{\ln\!\big(1 - \frac{PV\,i}{W(1+i)^{\delta}}\big)}{\ln(1+i)}

来源

  1. Microsoft Excel FV, PV, PMT and NPER functions (type 0 = end, 1 = start of period)
  2. Kellison, The Theory of Interest, 3rd ed., ch. 3 (annuities-immediate and annuities-due)

仅用于规划。贷款机构、税务机关和市场采用各自的舍入方式、费用和规则；作出承诺前，请向相关机构确认数值。

已对照来源验证

此计算器包含 8 个已解示例，答案来自独立来源。这些示例会在测试套件中运行，你也可以在此运行验证。

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