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Growing Annuity Future Value & Payment Timing

Model ordinary or beginning-of-period annuity payments, growing deposits and separate interest-compounding and payment frequencies.

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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

Three end-of-year payments starting at 100 and growing 10 percent each year accumulate to 363 when the annual interest rate is also 10 percent.

FV = P × [(1 + r)^n − (1 + g)^n]/(r − g) × (1 + r × timing); at r = g, replace the quotient by n × (1 + r)^(n − 1)

Worked example

Enter these known values and leave the other values blank.

First payment amount
100 USD
Annual nominal interest rate
10 %
Modeled annuity duration
3:0 yrs / mos
Payment growth per payment period
10 %
Future value at the modeled end
363 USD
Modeled payment count
3
Equivalent nominal rate at payment frequency
10 %
Interest rate per payment period
10 %

Assumptions and limitations

  • Payment growth applies once per payment period, not once per year unless payments are annual. The entered payment is the first payment.
  • Ordinary payments occur at period end; annuity-due payments occur at period beginning. Future value is measured at the end of the same n-period horizon.
  • Periodic interest is (1 + annual nominal rate/compounding frequency)^(compounding frequency/payment frequency) − 1; continuous compounding uses exp(annual rate/payment frequency) − 1.
  • Weekly and daily presets use 52.1775 and 365.242 periods per modeled year. Noninteger payment counts interpolate the formula, rather than describe a literal payment schedule.
  • The model retains limits of 1,000 years, 365,242 payments, and annual interest or per-payment growth at most 1,000 percent. Growth must exceed minus 100 percent; interest is nonnegative. No fees or taxes are deducted.

Common questions

What if payment growth equals the interest rate per period?

The quotient’s limit is n times (1 + r) to the power n − 1. This avoids the zero divided by zero in the ordinary formula.

Is growth entered per month or per year?

Per payment period. For monthly payments, enter the growth between consecutive monthly deposits.

References

Bookify uses the equal-growth-and-interest limit and zero-interest branches while retaining the available inverse equations. Bookify requires valid payment timing and positive payment frequencies, with payment growth above minus 100 percent per period.

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