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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.

Mis à jour Exemples vérifiés : 8

$
$
%
Nominal yearly rate, compounded once per payment period
Essayer
Future value
$
Future value: $205,516.83
Décimales : 2 ; Au plus proche, égalités vers le chiffre pair
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%Intérêts41.6%
Accumulation schedule Lignes : 20
AnnéeStart balancePaid inIntérêtsEnd 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
Comment le calcul est effectué 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

À propos de 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.

Exemples détaillés

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

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

Source de vérification : Future value annuity factor table, 5% and 10 periods: 12.5779; Python decimal 12,577.8925355…

Same payments as an annuity due

Je veux trouver
Future value of regular payments
Payment each period
1000
Starting balance
0
Term
10
Term in
Années
Interest rate (per year)
5%
Payments every
Année
Payments made at
Start (annuity due)
Future value
13,206.79

Source de vérification : 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

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

Source de vérification : 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%

Je veux trouver
Payout from a lump sum over a set time
Lump sum at the start
59,777.15
Term
20
Term in
Années
Interest rate (per year)
8%
Payments every
Mois
Payments made at
End (ordinary)
Payment each period
500.00

Source de vérification : Microsoft PV documentation: =PV(0.08/12, 12*20, 500, , 0) returns ($59,777.15)

Questions

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.

Quelle est la précision de « Annuity calculator (growth and payout) » ?

La précision dépend de vos données et des hypothèses de la méthode. Le calcul décimal utilise 50 chiffres significatifs, mais les estimations, méthodes numériques et données sources peuvent être moins précises ; l’arrondi affiché ne supprime pas ces limites. Exemples résolus vérifiés à partir de sources indépendantes : 8. Par exemple, « Future value of 1,000 a year for 10 years at 5% » est vérifié à l’aide de Future value annuity factor table, 5% and 10 periods: 12.5779; Python decimal 12,577.8925355….

D’où vient cette méthode ?

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).

À propos de ce calculateur

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)}

Sources

  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)

Pour la planification uniquement. Prêteurs, administrations fiscales et marchés appliquent leurs propres arrondis, frais et règles ; confirmez les chiffres auprès d’eux avant de vous engager.

Vérifié avec les références

Ce calculateur comprend 8 exemples résolus dont les réponses proviennent de sources indépendantes. Ils font partie de la suite de tests et peuvent aussi être exécutés ici.

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