Method
The rate covers the period you pick beside it (per year, quarter, month or day), and “interest added to balance” is how often the earned interest joins the balance and starts earning too. Picking a rate period sets the adding schedule to match; change it separately for quotes like “7% a year, added monthly”, where each monthly addition is 7% ÷ 12. The effective annual yield is (1 + r/n)^n − 1 for discrete compounding and e^r − 1 for continuous. Contributions are grown at the equivalent periodic rate (1 + EAR)^(1/p) − 1, so the yield is the same however often the account compounds. Where compounding is less frequent than contributions, this is a smooth approximation of a stepped credit — it will not tie out to a passbook that posts interest once a year.
Contributions change on each anniversary, so year one pays the amount you set and year t pays that amount stepped t−1 times; a negative raise shrinks payments and −100% stops them after year one. Doubling time is for the starting amount alone and ignores contributions; the Rule of 72 estimate sits beside the exact solve. Crossover is the first year where interest earned to date exceeds everything put in to date, starting amount included, once more than zero has gone in.
“Withdrawals, fees & tax” is one control for anything paid out of gains: money you withdraw, a performance fee or profit share, tax on gains. It takes a share of the profit — the growth since the last time it was taken, contributions not counted — at the end of each month, quarter or year, and only when that profit is positive. Enter one combined share: charges on the same profit add up (20% and 25% make 45%), while a charge on what an earlier one left compounds (a 20% fee, then 25% tax on the rest, makes 40%). Costs that are not a share of profit — a flat fee, or a yearly percentage of the balance — don’t fit this control; lower the return rate instead. What is taken out stops compounding, so the chart stacks it as a hatched band above the balance. The account is simulated period by period at the finer of the contribution schedule and this one; for terms past the simulated span, the last simulated year is raised to the remaining power.
There are no caps. Every year of any term comes from a closed form rather than a step-by-step loop, so a million-year term costs no more than a thirty-year one, and the schedule pages through every year of it. Figures past a 64-bit float’s range (about 1.8 × 10308) are carried as logarithms and shown in scientific notation, with only as many mantissa digits as the logarithm can vouch for. Crossover is found exactly across the first 10,000 years, then bracketed on a fine grid and bisected to the exact year. The only inputs refused are the ones with no arithmetic answer: a compounding period whose rate is −100% or lower (so the bound moves with frequency, and continuous compounding has none), inflation at or below −100%, and a term that is negative, fractional, or longer than a 64-bit number can count in whole years.
Not advice, and not a projection of any real account
These figures are fixed‑rate arithmetic, not a forecast. Real returns vary year to year and can be negative; spreads and slippage are not modelled, fees and tax only as far as you enter them as a share of profit, and no rate shown here is one MidasCode.AI offers, quotes or has achieved. Trading and investing carry substantial risk of loss and are not suitable for everyone. Past performance is not indicative of future results. Nothing on this page is investment advice, a solicitation, or an offer to manage funds — MidasCode.AI builds and operates trading technology.
A tool from MidasCode.AI — trading systems and quant infrastructure. See the full risk disclosure.