How the math works
Horizon Compound steps forward one contribution at a time and uses that same recurrence for the yearly table and the CSV. There is not a second, hidden formula behind the download.
Rate convention
The percentage is a nominal annual rate. Five means 5 percent per year. It is not already an effective annual yield, and it is not a decimal such as 0.05. For monthly compounding, the periodic rate is 0.05 divided by 12. Daily compounding uses 365 periods in a year, not 365.25. Continuous compounding grows by e raised to rate times time and does not divide the rate into periods.
Contribution timing
The contribution is a fixed amount, paid once a year, each quarter, each month, every two weeks (26 times a year), or each week (52 times a year). “End of each period” adds the money after that period’s growth, so the new contribution does not earn interest until later periods. “Beginning of each period” adds it first, so it earns interest during the period. Years are whole numbers, and each year contains the same number of contributions.
When the frequencies differ
Each contribution period multiplies the balance by (1 + rate / n) raised to (n / m). Here n is the number of compounding periods per year and m is the number of contributions per year. Continuous compounding uses e raised to (rate / m) instead. A weekly contribution with monthly compounding therefore grows by (1 + rate / 12) raised to (12 / 52) on every week. The timing choice decides whether the contribution is added before or after that growth.
Zeros and limits
A zero rate earns no interest. The ending balance is the starting balance plus every contribution, with no rounding dust. Zero years leaves the starting balance untouched and adds nothing; the CSV then contains only the header. Amounts cannot be negative. The starting balance stops at 1,000,000,000,000, each contribution stops at 1,000,000,000, the rate stops at 100 percent, and the duration stops at 80 years. If a combination would push the balance past 100,000,000,000,000, where cents are no longer trustworthy in ordinary computer arithmetic, the page shows an error instead of a fake precise total.
What this estimate leaves out
Taxes, fees, inflation, missed deposits, and rate changes are left out. Displayed amounts are rounded half away from zero to the nearest cent. The CSV keeps eight decimal places of the same recurrence. This is an educational estimate. It is not a forecast, not a guarantee, and not personal investment advice.
Privacy
The numbers stay in this browser. Horizon Compound does not upload them, does not store an account, and does not send them to an analytics service. The CSV is built on this device and saved through your browser’s download. Fonts are part of the page files. Reloading the tab clears the fields back to the worked example that ships with the page.