Guide
How compound interest works
Compound interest is interest that starts earning interest. You earn a return on the original amount. If that return stays invested, the next period pays you on both.
The idea is simple. The assumptions are where people get misled.
A fixed rate is only a model
A bank rate can change. An MPF fund moves up and down, and it is not a savings account with a promised rate. A US index fund charges an expense ratio, and dividends in a taxable account are not treated the same way as dividends in a retirement account.
The compound interest calculator answers a narrower question. If a rate stayed constant, and you added the same amount at the end of every compounding period, what would the balance be?
The formula on this site
When the rate per period is not zero:
FV = P × (1 + i)^n + PMT × [((1 + i)^n − 1) / i]
When the rate is zero, interest is zero:
FV = P + PMT × n
P is the principal. PMT is the contribution at the end of each compounding period. i is the annual rate divided by the number of compounds per year. n is that number of compounds multiplied by the years. Interest earned is FV minus P minus every contribution.
Two checks you can do on paper: 1,000 at 5% compounded once a year for one year, with nothing added, is 1,050. 1,000 at 10% compounded annually for two years is 1,210.
Why the contribution timing matters
This site adds each contribution at the end of the period (an ordinary annuity), and the contribution schedule matches the compounding schedule. Money added at the start of the period would earn one extra period of interest. A calculator that mixes those conventions will not match this one, even when the headline rate looks the same.
Daily compounding uses 365 periods every year, including leap years, so two calendar years stay comparable.
What to read next to the number
Hong Kong salaries tax is published by the Inland Revenue Department. MPF rules and your own fund prices sit with the Mandatory Provident Fund Schemes Authority and your scheme, not inside a fixed-rate formula. A bank mortgage illustration includes insurance and fees that this math ignores.
CalcIsland will add pages for MPF, salaries tax, mortgages, and US investing basics. Those pages can link back here for the compounding step. None of them, including this one, replace your statements or a licensed adviser.