Compound Interest
For a starting balance P, monthly contribution C, annual rate r (decimal), years t, and compounding n times per year, we compute the future value as:
FV = P · (1 + r/n)^(n·t) + C · [((1 + r/n)^(n·t) − 1) / (r/n)] · (n/12)When contributions are set to monthly, they are treated as deposits at the end of each month. When compounding is set to yearly, monthly contributions are still recorded monthly but interest is only applied once per year, matching how many high-yield savings accounts and bonds behave.
Simple Interest
Simple interest uses the classic formula I = P · r · t. No contributions are added.
Savings Goal (reverse solve)
Given a target amount, rate, and time horizon, we solve the future-value formula for the required monthly contribution using the same compounding logic as above.
Investment Calculator: inflation and tax
Real value is computed as FV / (1 + i)^t, where i is your inflation assumption. This tells you what your future balance buys in today's money.
After-tax value assumes taxes apply only to accrued interest, not principal or contributions: After-tax = Contributions + Interest · (1 − taxRate). This is a simplification — real tax treatment depends on account type (taxable brokerage, IRA, ISA, etc.) and your jurisdiction.
The three-scenario view (pessimistic / expected / optimistic) uses the rate you set as the expected case, and by default adjusts ±3 percentage points. This is a rough sensitivity check, not a probabilistic forecast.
Growth Insights
- Rule of 72: doubling time ≈
72 / rate. Accurate within ~0.5 years for rates between 6% and 10%. - Milestones are read directly from the year-by-year balance series — the first year the balance crosses each threshold.
- Contribution vs Growth = interest ÷ final balance. Includes accrued interest on both the starting balance and monthly deposits.
- Plan Health Summary is a rule-based sanity check based on horizon, monthly amount, and return realism. It is not personalised financial advice.
Default assumptions
- Inflation defaults to 2.5% — the long-run average for developed economies.
- Contributions are made at the end of each month.
- No fees, no bid/ask spread, no rebalancing costs are modelled.
- Rates are entered as an annual percentage; the tool does not convert APR ↔ APY automatically.
- Guides compound monthly with month-end deposits unless a section says otherwise (for example "compounded once a year").
Savings interest vs. investment returns
- Savings interest (APY) is what a bank or deposit account pays. It is variable, can fall at any time, and is usually well below 6%.
- Investment returns such as the 7% used in many guides are a hypothetical long-run average for a diversified stock portfolio. They are not guaranteed and individual years can be negative.
- Guides label which kind of rate each figure uses; scenario guides that rely on investment returns show an assumptions note at the top.
What we deliberately do not model
- Sequence-of-returns risk (relevant for retirement drawdown).
- Market volatility (variance around the expected rate).
- Currency conversion — you pick a currency for display, but math is currency-neutral.
- Personal factors: risk tolerance, dependants, insurance, debt, emergency fund.
Data sources and references
- Historical stock returns: S&P 500 total return series, 1928–present.
- Inflation baseline: US Bureau of Labor Statistics CPI-U, long-run average.
- Formulas: standard time-value-of-money textbook derivations.
Corrections
Spot a bug or want to challenge an assumption? Contact us — we log every correction and re-check the affected calculator.