# 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.

ਇੰਟਰਐਕਟਿਵ ਰੂਪ: https://www.calcopenly.com/pa/finance/annuity-calculator
ਵਿਸ਼ਾ: ਵਿੱਤੀ ਕੈਲਕੁਲੇਟਰ

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.

## ਇਨਪੁੱਟ

- **ਮੈਂ ਪਤਾ ਕਰਨਾ ਚਾਹੁੰਦਾ ਹਾਂ** (ਚੋਣਾਂ: Future value of regular payments, Payout from a lump sum over a set time, How long a lump sum lasts)
- **Payment each period**
- **Starting balance**
- **Lump sum at the start**
- **Withdrawal each period**
- **Term**
- **Term in** (ਚੋਣਾਂ: ਸਾਲ, ਮਹੀਨੇ)
- **Interest rate (per year)**: Nominal yearly rate, compounded once per payment period
- **Payments every** (ਚੋਣਾਂ: Week, Two weeks, ਮਹੀਨਾ, Quarter, Half-year, ਸਾਲ)
- **Payments made at** (ਚੋਣਾਂ: End (ordinary), Start (annuity due))

## ਨਤੀਜੇ

- Future value — ਮੁੱਖ ਨਤੀਜਾ
- Payment each period
- Money lasts (years)
- Number of payments
- Final partial payment
- Present value of the payments
- Total of all payments
- Interest earned
- Rate per period

## ਫਾਰਮੂਲਾ

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

## ਹੱਲ ਕੀਤੀਆਂ ਉਦਾਹਰਨਾਂ

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

- ਮੈਂ ਪਤਾ ਕਰਨਾ ਚਾਹੁੰਦਾ ਹਾਂ: Future value of regular payments
- Payment each period: 1000
- Starting balance: 0
- Term: 10
- Term in: ਸਾਲ
- Interest rate (per year): 5%
- Payments every: ਸਾਲ
- Payments made at: End (ordinary)
- **Future value: 12,577.89**
- **Total of all payments: 10,000.00**
- **Interest earned: 2,577.89**
- ਜਾਂਚ ਦਾ ਸਰੋਤ: Future value annuity factor table, 5% and 10 periods: 12.5779; Python decimal 12,577.8925355…

### Same payments as an annuity due

- ਮੈਂ ਪਤਾ ਕਰਨਾ ਚਾਹੁੰਦਾ ਹਾਂ: Future value of regular payments
- Payment each period: 1000
- Starting balance: 0
- Term: 10
- Term in: ਸਾਲ
- Interest rate (per year): 5%
- Payments every: ਸਾਲ
- Payments made at: Start (annuity due)
- **Future value: 13,206.79**
- ਜਾਂਚ ਦਾ ਸਰੋਤ: 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

- ਮੈਂ ਪਤਾ ਕਰਨਾ ਚਾਹੁੰਦਾ ਹਾਂ: Future value of regular payments
- Payment each period: 200
- Starting balance: 500
- Term: 10
- Term in: ਮਹੀਨੇ
- Interest rate (per year): 6%
- Payments every: ਮਹੀਨਾ
- Payments made at: Start (annuity due)
- **Future value: 2,581.40**
- ਜਾਂਚ ਦਾ ਸਰੋਤ: 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%

- ਮੈਂ ਪਤਾ ਕਰਨਾ ਚਾਹੁੰਦਾ ਹਾਂ: Payout from a lump sum over a set time
- Lump sum at the start: 59,777.15
- Term: 20
- Term in: ਸਾਲ
- Interest rate (per year): 8%
- Payments every: ਮਹੀਨਾ
- Payments made at: End (ordinary)
- **Payment each period: 500.00**
- ਜਾਂਚ ਦਾ ਸਰੋਤ: Microsoft PV documentation: =PV(0.08/12, 12*20, 500, , 0) returns ($59,777.15)

### Excel PMT example: 10,000 over 10 months at 8%

- ਮੈਂ ਪਤਾ ਕਰਨਾ ਚਾਹੁੰਦਾ ਹਾਂ: Payout from a lump sum over a set time
- Lump sum at the start: 10,000
- Term: 10
- Term in: ਮਹੀਨੇ
- Interest rate (per year): 8%
- Payments every: ਮਹੀਨਾ
- Payments made at: End (ordinary)
- **Payment each period: 1,037.03**
- ਜਾਂਚ ਦਾ ਸਰੋਤ: Microsoft PMT documentation: =PMT(8%/12, 10, 10000) returns ($1,037.03)

### How long 100,000 lasts at 6% with 1,000 a month

- ਮੈਂ ਪਤਾ ਕਰਨਾ ਚਾਹੁੰਦਾ ਹਾਂ: How long a lump sum lasts
- Lump sum at the start: 100,000
- Withdrawal each period: 1000
- Interest rate (per year): 6%
- Payments every: ਮਹੀਨਾ
- Payments made at: End (ordinary)
- **Number of payments: 138.98**
- **Money lasts: 11.58 years**
- **Final partial payment: 975.78**
- ਜਾਂਚ ਦਾ ਸਰੋਤ: Python decimal: −ln(1 − 100,000 × 0.005/1,000)/ln 1.005 = 138.9757 months; period-by-period simulation for the final payment

## ਸਵਾਲ

### 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)” ਕਿੰਨਾ ਸਟੀਕ ਹੈ?

ਸਟੀਕਤਾ ਤੁਹਾਡੇ ਇਨਪੁੱਟਾਂ ਅਤੇ ਵਿਧੀ ਦੀਆਂ ਧਾਰਨਾਵਾਂ ਉੱਤੇ ਨਿਰਭਰ ਕਰਦੀ ਹੈ। ਦਸ਼ਮਲਵ ਗਣਨਾ 50 ਮਹੱਤਵਪੂਰਨ ਅੰਕ ਵਰਤਦੀ ਹੈ, ਪਰ ਅਨੁਮਾਨ, ਅੰਕੀ ਵਿਧੀਆਂ ਅਤੇ ਸਰੋਤ ਡਾਟਾ ਘੱਟ ਸਟੀਕ ਹੋ ਸਕਦੇ ਹਨ; ਦਿਖਾਏ ਮੁੱਲਾਂ ਨੂੰ ਗੋਲ ਕਰਨ ਨਾਲ ਇਹ ਹੱਦਾਂ ਦੂਰ ਨਹੀਂ ਹੁੰਦੀਆਂ। ਸੁਤੰਤਰ ਸਰੋਤਾਂ ਦੀਆਂ ਹੱਲ ਕੀਤੀਆਂ ਉਦਾਹਰਨਾਂ ਨਾਲ ਜਾਂਚ: 8। ਉਦਾਹਰਨ ਲਈ, “Future value of 1,000 a year for 10 years at 5%” ਦੀ ਜਾਂਚ Future value annuity factor table, 5% and 10 periods: 12.5779; Python decimal 12,577.8925355… ਨਾਲ ਕੀਤੀ ਜਾਂਦੀ ਹੈ।

### ਇਸ ਵਿਧੀ ਦਾ ਸਰੋਤ ਕੀ ਹੈ?

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).

## ਸਰੋਤ

- [Microsoft Excel FV, PV, PMT and NPER functions (type 0 = end, 1 = start of period)](https://support.microsoft.com/office/pv-function-23879d31-0e02-4321-be01-da16e8168cbd)
- Kellison, The Theory of Interest, 3rd ed., ch. 3 (annuities-immediate and annuities-due)

_ਸਿਰਫ਼ ਯੋਜਨਾਬੰਦੀ ਲਈ। ਕਰਜ਼ਦਾਤੇ, ਟੈਕਸ ਅਧਿਕਾਰੀ ਅਤੇ ਬਾਜ਼ਾਰ ਆਪਣੇ ਅੰਕ ਗੋਲ ਕਰਨ ਦੇ ਢੰਗ, ਫ਼ੀਸਾਂ ਅਤੇ ਨਿਯਮ ਲਾਗੂ ਕਰਦੇ ਹਨ; ਵਚਨਬੱਧ ਹੋਣ ਤੋਂ ਪਹਿਲਾਂ ਉਨ੍ਹਾਂ ਨਾਲ ਅੰਕੜੇ ਪੱਕੇ ਕਰੋ।_