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Growing Annuity Payment Present Value

Discount a finite sequence of growing payments with beginning or end payment timing and selected compounding.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

Two annual end payments of 100 at 10% interest and zero growth have present value 173.5537190083. Moving both to the beginning increases it to 190.9090909091.

PV = payment × [1 − ((1+g)/(1+i))^N]/(i−g) × (1+i × due flag).

Worked example

Enter these known values and leave the other values blank.

Payment frequency
Yearly
Compound frequency
Yearly
Type of annuity
Ordinary annuity
Payment amount
100 USD
Interest rate
10 %
Growth rate of annuity
0 %
Annuity term
2:0 yrs / mos
Present value of annuity
173.55 USD
Number of periods
2
Equivalent interest rate
10 %
Periodic equivalent interest rate
10 %

Assumptions and limitations

  • Payments grow each payment period by the entered growth fraction. Selected interest compounding is converted to the payment period.
  • The captured finite formula requires periodic interest different from growth; the equal-rate limit is excluded. This is a mathematical cash-flow scenario, not an annuity product quote.
  • Enter all monetary amounts in a single currency. Retained currency conversion factors are a captured static snapshot, not live exchange rates.
  • Clear a known field before solving for it. Locks retain chosen inputs; inconsistent locked values need correction. Reset restores the captured defaults.

Common questions

What does the worked example show?

Two annual end payments of 100 at 10% interest and zero growth have present value 173.5537190083. Moving both to the beginning increases it to 190.9090909091.

What assumptions limit this calculation?

Payments grow each payment period by the entered growth fraction. Selected interest compounding is converted to the payment period.

References

Use the documented finite scenario domain. annuityTerm must be positive. Use nonnegative interest. Payment growth must exceed minus 100 percent. Equal growth and periodic discount rate require a separate limit. Payment cannot be negative. Translate the captured equivalent-rate helper into local arithmetic. Continuous compounding uses mathematical exp rather than a rounded double-precision e constant; periodic compounding and every retained inverse are preserved.

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