Scope
MoneyMaths is an independent educational calculator project. Results are estimates from user-supplied values. We do not claim professional financial accreditation or independent expert certification. Currency selection on the decision planners changes labels only; all amounts must use the same currency.
Loan payments
For principal P, monthly rate r and n payments, the monthly payment is P × r ÷ (1 − (1 + r)−n). At 0%, it is P ÷ n. The nominal annual rate is divided by 12. Interest is applied to the remaining balance before each monthly payment.
Loan comparison adds separately paid upfront fees to total repayments. It does not compute APR, present value or refinancing break-even. Extra-payment comparisons apply a lump sum at the start and retain the original scheduled monthly payment. The final payment is capped at the balance plus interest.
Debt repayment
The budget is the sum of entered minimums on positive balances plus extra payment. Interest accrues once per month; minimum payments are allocated first. The remaining budget goes to the selected priority order. Paid-off debts release their payment into that same fixed budget. Unpaid interest is added to the balance.
Debt identities remain attached to their results even when payment priority changes. A simulation stops after 600 months and explicitly reports an unfinished balance rather than inventing a payoff date. Actual lenders may use daily interest, changing minimums or different capitalization rules.
Compound growth and savings targets
For nominal annual rate a compounded k times a year, the equivalent monthly rate is (1 + a/k)k/12 − 1, where a is expressed as a decimal. Both the initial deposit and monthly contributions use this same basis. Contributions occur at month end.
For monthly rate r and n months, the projected balance is P × (1+r)n + C × ((1+r)n−1)/r. At 0%, it is P + C × n. The savings planner solves this equation for C and floors the required contribution at zero. Return scenarios are sensitivity examples, not probability forecasts.
Other tools
The mortgage tool is a simplified US-style model. Its lifetime extras assume unchanged tax, insurance, HOA and PMI amounts; PMI is held constant across the term, so total cost can overstate a loan where PMI ends earlier. The retirement tool’s 4% withdrawal estimate is an illustration, not a safe-income guarantee. Inflation uses a constant user-entered rate, not historical CPI data.
Validation and rounding
Decision planners reject incomplete inputs, negative balances and invalid terms. They support up to 50 years and whole-month periods. Calculation tests check zero-interest cases, known payment amounts, lump sums, payment-budget conservation, debt-name mapping, unpaid interest and compounding-frequency effects. Amounts are calculated at full precision and rounded for display; lender-specific cent rounding can differ.
Sources and corrections
For terminology, see the CFPB explanation of APR and interest. For growth inputs, see Investor.gov. These references do not endorse this site.
Report a calculation problem with the tool name, non-sensitive example inputs and expected result. Avoid account numbers or identifying financial details.
Methodology updated 21 September 2026.