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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.

Diperbarui Contoh terverifikasi: 8

$
$
%
Nominal yearly rate, compounded once per payment period
Coba
Future value
$
Future value: $205,516.83
Tempat desimal: 2; Terdekat, jika berjarak sama menuju digit genap
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%Bunga41.6%
Accumulation schedule Baris: 20
TahunStart balancePaid inBungaEnd 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
Cara menghitung 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

Tentang 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.

Contoh penyelesaian

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

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

Sumber pemeriksaan: Future value annuity factor table, 5% and 10 periods: 12.5779; Python decimal 12,577.8925355…

Same payments as an annuity due

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

Sumber pemeriksaan: 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

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

Sumber pemeriksaan: 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%

Saya ingin mencari
Payout from a lump sum over a set time
Lump sum at the start
59,777.15
Term
20
Term in
Tahun
Interest rate (per year)
8%
Payments every
Bulan
Payments made at
End (ordinary)
Payment each period
500.00

Sumber pemeriksaan: Microsoft PV documentation: =PV(0.08/12, 12*20, 500, , 0) returns ($59,777.15)

Pertanyaan

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.

Seberapa akurat “Annuity calculator (growth and payout)”?

Akurasi bergantung pada masukan dan asumsi metode. Aritmetika desimal memakai 50 digit signifikan, tetapi perkiraan, metode numerik dan data sumber bisa kurang presisi; pembulatan yang ditampilkan tidak menghilangkan batasan itu. Contoh penyelesaian yang diperiksa dengan sumber independen: 8. Misalnya, “Future value of 1,000 a year for 10 years at 5%” diperiksa dengan Future value annuity factor table, 5% and 10 periods: 12.5779; Python decimal 12,577.8925355….

Dari mana metode ini berasal?

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).

Tentang kalkulator ini

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)}

Sumber

  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)

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Diperiksa dengan referensi

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