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Monthly Investment & Lump-Sum Constant-Return Model

Compare beginning-of-month contributions with a one-time investment under a supplied nonnegative constant-return assumption.

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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

A beginning-of-month investment of 100 for two months at a nominal annual rate of 12% gives 203.01. At zero return it gives 200.

Monthly mode: FV = D[(1+i)^N − 1](1+i)/i; one-time mode: FV = P(1+r)^years

Worked example

Enter these known values and leave the other values blank.

Beginning-of-month contribution
100 USD
Assumed annual rate (%) — see mode convention
12 %
Investment period
2 yrs / mos
Projected monthly-investment value
203.01 USD

Assumptions and limitations

  • Monthly mode uses a nominal annual rate divided by twelve and contributions at the beginning of each month. One-time mode uses annual compounding.
  • This retained model accepts nonnegative rates and amounts. It excludes losses, volatility, fees, taxes and changes in contributions, so it does not represent the full range of possible mutual-fund outcomes.
  • Time is positive. Fractional payment periods are a mathematical extension and do not describe a dated transaction schedule.
  • At zero return, the monthly result is the sum of contributions and the one-time result is the original amount.

Common questions

Does this predict what a fund will earn?

No. The entered constant rate is an assumption. Actual investment returns can vary and can be negative.

Why is the monthly result larger than an end-of-month model?

Contributions arrive at the start of each month and therefore earn an extra month of return.

References

Bookify accepts zero contributions and returns and requires a positive investment duration. Bookify evaluates the zero-interest limit directly, including available reverse calculations; nonzero-rate source expressions are preserved.

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