Future Value of Periodic Contributions to an Index Fund
Summary
The document asks how to calculate the future value of an account funded by an initial contribution and regular additions, given a share price, a constant annual return, and a fixed number of periods. The response concludes that the ordinary or due annuity formulas can be used even when the investment is described in terms of share-price growth rather than account-value growth.
The answer also notes that tracking the number of shares purchased over time can help explain how the account accumulates. It does not provide the derivation, a worked formula, or a numerical example, and it assumes away taxes, fees, volatility, and other complications. Thus, it offers a simplified conceptual resolution for fixed contributions and a constant return, rather than a model of actual fund performance or variable investment outcomes.
Key ideas
- Annuity formulas can represent the future value of fixed periodic contributions under a constant return assumption.
- The timing of contributions determines whether an ordinary annuity or an annuity due is appropriate.
- Account accumulation can also be understood by tracking the shares acquired with each contribution.
- The simplified setup excludes taxes, expenses, volatility, and other real-world effects.
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Full text
# How to simply calculate future value of periodic contributions to an index fund account? # How to simply calculate future value of periodic contributions to an index fund account? So, for the sake of simplicity, ignoring taxes, expense ratio, volatility or anything else other than known values for the following five variables: - Starting contribution (dollars) - Annual contribution (dollars, deposited at the beginning or end of each period) - Starting price of one index fund share (example, VTSAX is currently $118.10) - Annual return of one index fund share (example, 10%, so in a year VTSAX would be $129.91 per share) - Number of periods (example, 30, as in years, to keep it simple) Which is the most practical equation you know of that can be used to calculate the future value of contributions to an index fund account after n periods (say, 30 years)? The annuity (ordinary or due) formula gets me part of the way there but does not take share price into account. So I'm looking for a formula that does without requiring values for too many additional variables, if any. If there isn't an equation well-suited for this out there, I might think about deriving one. No formal finance training, self-taught as I go. Thx, Rec ## Answer by recisuser (score 0, accepted) https://quant.stackexchange.com/a/69321 I ended up figuring it out. Long story short, the annuity formulas (ordinary or due) can in fact get the job done, whether the share price or the capital value of the account itself compounds at the annual return rate makes no difference. But it's still helpful to see how the number of shares increase over n periods.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.