Will I hit my goal?

A start amount, a monthly saving and a guess at returns. We play out 5,000 possible futures, month by month, and count how often you get there.

Working it out…

$5,000 to start and $500 a month in a stock index fund for 20 years, at 7% a year with 15% swings. The goal: $250,000. Made-up assumptions. Past returns don’t promise future ones.

Start with

Add each month

For how many years

Your goal

Average yearly return

Typical yearly swing

The swing is the volatility: how far a typical year lands from the average, up or down. A savings account barely swings; stocks swing a lot.

Playing out 5,000 futures…

How this works, step by step

Start with a guess about returns.
You give two numbers: the average yearly return, and how much a typical year swings around it, called volatility. Both are assumptions, not facts. A savings account pays a steady rate. A stock fund might average 7% over decades, but any single year can be up 25% or down 30%.
Play out one month.
Each month the balance grows by a random amount: usually a little, sometimes a lot, sometimes it shrinks. Then your monthly saving goes in. The random growth is set up so that, on average, a year grows by exactly your average return.
next = balance × e^(μ + s × z) + monthly · s = volatility ÷ √12 · μ = ln(1 + return) ÷ 12 − s² ÷ 2 · z is a random draw from the bell curve
Repeat for every month, then 5,000 times.
Twenty years is 240 months, so one future is 240 random steps. That is one way things could go. Play it out 5,000 times and the futures spread into a fan: narrow at the start, wider every year, because surprises pile up. This is a Monte Carlo simulation.
Read the fan.
At every year, line up the 5,000 balances from lowest to highest. The one a tenth of the way in is the bad case, the middle one is the middle, and the one nine tenths in is the good case. The shaded band holds 8 futures in 10. Your chance of reaching the goal is the share of futures that end at or above it.
chance of reaching the goal = futures ending at or above it ÷ 5,000
The average is not the typical.
Big swings help a few futures a lot and hurt many a little, so the average sits above the middle. In the riskier example the average ends near $201,000, right at the goal, yet only about 1 in 3 futures get there, and the middle one ends well short of it, around $140,000. Plan on the middle and the bad case, not the average.
average final = start × (1 + return)^years + monthly × (g^months − 1) ÷ (g − 1), with g = (1 + return)^(1/12)

What this leaves out

These are made-up assumptions, and past returns don’t promise future ones. Real markets have worse crashes than this model draws, and good and bad years tend to bunch together. There are no fees, taxes or inflation here, and every month’s saving goes in without fail.

Use it to see how the range widens with risk and with time, and how much a bigger monthly saving moves the bad case. For learning, not financial advice.

For learning, not financial, medical or betting advice.

Try it with your own numbers