Compound Growth: Compare Time, Contributions and Assumptions

Key Takeaways:

Compounding describes growth on earlier growth; it does not establish a future investment return.
Separate your contributions from projected earnings when comparing scenarios.
Check the rate, compounding frequency, fees, taxes and inflation before interpreting a forecast.

A compound-growth calculation is useful when you want to understand how a set of assumptions interacts over time. It becomes misleading when an assumed rate is presented as something an investment will deliver.

Start with a simple model you can explain. Add complexity only when you understand what each change does to the result.

See the arithmetic before adding a forecast

Suppose a fictional $1,000 balance earns exactly 5% each year, credited annually, with no contributions, withdrawals, fees or taxes. After one year the balance is $1,050. After two years it is $1,102.50. The second year’s $52.50 increase includes $2.50 earned on the first year’s growth.

That example illustrates arithmetic under a fixed assumption. It is not an available product rate or a prediction about stocks. For a single starting amount with annual compounding, the formula is starting balance multiplied by (1 + annual rate) raised to the number of years.

Separate deposits from modeled growth

A projected balance may look impressive because it includes many years of contributions. If you start with $1,000 and add $100 a month for ten years, your total contributions are $13,000, before any growth. Compare that contribution total with the model’s ending value.

Also state when contributions occur. A beginning-of-month deposit has a different time in the model from an end-of-month deposit. Use the same convention when comparing two scenarios.

Change one assumption at a time

First compare different contribution amounts using the same rate and time period. Next compare different saving periods using the same contribution. Finally compare a range of assumed rates. This shows whether the projected improvement comes from money you add, additional time or more optimistic assumptions.

Do not select a higher return merely to make a goal appear affordable. If a plan works only at that rate, record the dependence explicitly and consider alternatives within your control, such as the contribution, goal amount or deadline.

Distinguish a smooth illustration from investing

A fixed-rate calculator follows a smooth mathematical path. Market investments can lose value, and the sequence of returns matters when contributions or withdrawals occur. An average annual rate does not reproduce every possible path to an ending balance.

Use a calculator to learn about assumptions, then evaluate the actual investment’s risks, expenses and terms separately. Do not treat an illustration as a guarantee that a particular amount will be available on a particular date.

Check what the ending balance leaves out

Determine whether the rate is before or after fees and whether the output includes taxes. Label values as future dollars or purchasing power in today’s dollars. A larger future balance does not necessarily buy proportionately more if prices also increase.

The SEC’s Investor.gov calculator allows an initial investment, recurring contributions, a time period, an estimated rate, a rate range and a compounding frequency. Save those inputs with your output. The comparison is useful only if you can later identify the assumptions that produced it.