Savings
More terms
The fee is a share of the balance taken each year, such as a fund’s expense ratio. Inflation turns future dollars into today’s dollars: what they would buy now.
Scenarios
optionalReturns change from year to year. The scenarios show the same plan at a steady lower and higher return, in percentage points around the expected one.
Balance by year
Return scenarios
Year by year
Interest factors
F is a future amount, P a present amount, A an equal amount at the end of each period, and G the amount by which each period’s flow grows (an arithmetic gradient). Multiply the known amount by the factor: for example F = P × (F/P, i, n).
Basis of the numbers
Each period the balance, plus any contribution made at the start of the period, earns the rate per period: (1 + r/m)m/p − 1 for a yearly rate r compounded m times a year with p contributions a year, or er/p − 1 when it compounds continuously. The yearly fee is taken in equal parts: each period the balance is multiplied by (1 − fee)1/p. A contribution made at the end of a period earns nothing that period. Contributions rise by the yearly increase at the start of each year. Today’s dollars divide each balance by (1 + inflation)t, with t in years.
A contribution or starting amount needed is found exactly, since the ending balance is in direct proportion to each; a return needed is found by bisection; a time needed is the first period whose balance reaches the goal. Results are estimates for planning, not investment advice: real returns, fees and inflation change from year to year.
Estimates for planning only, not investment advice. Example values are illustrative. Nothing you enter leaves this page.