Hong Life CalculatorsUnderstanding the investment calculator — concept and principle
This calculator projects how a starting sum and regular monthly contributions grow at a steady annual return. It also shows what the final balance is worth in today's money after inflation. Use it to plan retirement saving, an index-fund habit or any long-term goal.
How it is calculated
- Monthly rate: i = (1 + r)^(1/12) − 1, where r is the expected annual return, so twelve months compound exactly to r.
- Starting amount after n months: P × (1 + i)^n.
- Monthly contributions: PMT × ((1 + i)^n − 1) ÷ i, multiplied by (1 + i) if you pay at the start of each month.
- Final balance = the two parts added. Total you put in = P + PMT × n; growth = balance − total put in.
- In today's money = balance ÷ (1 + inflation)^years.
The principle
Compounding means each month's gain is added to the balance and earns returns itself. A single sum grows along a geometric curve. A stream of equal deposits is the sum of many such curves, which collapses into the annuity formula above. Converting the annual return to an equivalent monthly rate keeps a 6% annual return exactly 6% a year, rather than the slightly higher figure from dividing by 12. Dividing by cumulative inflation turns future dollars into dollars with today's buying power.
Worked example
Default inputs: 10,000 USD start, 500 USD a month, 6% a year, 20 years, contributions at the end of each month, inflation 2.5%.
- n = 240 months; i = 1.06^(1/12) − 1 ≈ 0.48676%.
- Starting amount grows to 10,000 × 1.0048676^240 ≈ 32,071.35 USD.
- Contributions grow to 500 × (1.0048676^240 − 1) ÷ 0.0048676 ≈ 226,719.32 USD.
- Final balance ≈ 258,790.67 USD. You put in 10,000 + 500 × 240 = 130,000.00 USD, so growth is 128,790.67 USD.
- In today's money: 258,790.67 ÷ 1.025^20 ≈ 157,932.43 USD.
- Along the way: 48,125.15 USD after 5 years and 99,145.20 USD after 10 years.
| Years | Final balance |
|---|---|
| 5 | $48,125.15 |
| 10 | $99,145.20 |
| 15 | $167,421.53 |
| 20 | $258,790.67 |
| 25 | $381,063.19 |
| 30 | $544,691.40 |
| 40 | $1,056,696.06 |
How to read the result
Compare the growth with what you put in: over long periods growth often overtakes contributions, which shows why starting early matters. The inflation-adjusted figure is the better guide to future spending power. Try several return rates, such as a cautious and an optimistic one, to see a range rather than one number.
Common mistakes
- Treating the expected return as guaranteed. Real markets rise and fall from year to year.
- Ignoring fees and taxes, which reduce the effective return.
- Comparing the nominal final balance with today's prices.
- Mixing up contributions at the start and the end of each month.
Frequently asked questions
What annual return should I assume?
There is no safe single number. Use a range and remember that past returns do not guarantee future ones.
Does contributing at the start of the month matter?
Yes, slightly. Each deposit earns one extra month of growth.
Why show the balance in today's money?
Prices rise over time, so a future balance buys less. Deflating it shows its buying power now.
Sources: Brealey, Myers & Allen, Principles of Corporate Finance (future value and annuities) · US SEC Investor.gov, Compound Interest Calculator and guidance