Setting goals and deciding under uncertainty
A financial goal is a target amount by a date. Reaching it depends on how much is saved, how long there is, and what the money earns, and the last of these is uncertain. This lesson turns goals into monthly amounts, shows how to fit several goals into one budget, and then tests a goal with a deadline against the real history of US stocks and a savings account. A calculator counts, in every historical window of the chosen length, how often saving into stocks reached the goal. It shows that a higher average can still miss the date.
- Level
- Beginner
- Reading time
- About 26 minutes
- Know this first
- Tax planning and evasion
By the end you will be able to:
- write a goal with an amount, a date and a monthly saving
- fit several goals into one budget and decide what to move
- count how often a risky choice reached a goal in historical windows
- tell a higher average outcome from a better chance of meeting a deadline
- say why historical windows are not probabilities
From a wish to a plan
“I want to buy a home” is a wish. “I want $50,000 in eight years, which means saving a set amount each month” is a plan, because it can be checked. The earlier lessons in this module built the parts: a balance sheet, a budget, an emergency fund, a way to repay debt, insurance, a retirement plan and a view of tax. This last lesson puts them to use. It turns goals into monthly amounts, fits several goals into one budget, and then deals with the hard part: the money a goal depends on does not earn a certain return.
The lesson uses an invented household and real annual returns of the S&P 500, including dividends, for 2000 to 2024. It does not tell anyone what to invest in. It shows how to test a plan against history, and why the result can be a number of windows rather than a promise.
Writing a goal that can be checked
A useful goal has four parts. It names a target amount. It has a date. It states the monthly saving that follows from the first two. And it has a priority against the household’s other goals. Without a date, there is no way to tell whether the saving is enough. Without a priority, every goal competes for the same money and none is finished.
The saving needed comes from the same arithmetic as the retirement lesson. If a goal of $T is to be reached in N years by saving a fixed amount each year, earning a steady return r, the yearly saving is T divided by the sum of growth factors, ((1 + r)N − 1) ÷ r. The lesson uses a savings account paying 3% a year, an invented rate, and adds each year’s saving at the end of the year.
Several goals, one budget
The household from the earlier lessons has $1,000 a month for saving: the $800 saving goal in the budget lesson plus the $200 that was left unassigned. It has three goals. It wants to top up its emergency fund from $2,400 to $9,000, which is $6,600 more, in two years. It wants to replace its car, $15,000, in four years. And it wants a $50,000 house deposit in eight years.
| Goal | Target, $ | Years | Saving needed a month at 3%, $ |
|---|---|---|---|
| Top up the emergency fund | 6,600 | 2 | 271 |
| Replace the car | 15,000 | 4 | 299 |
| House deposit | 50,000 | 8 | 469 |
| Total a month | 71,600 | 1,038 |
The three goals need $271, $299 and $469 a month, which is $1,038 in total. That is $38 more than the $1,000 available, so the plan does not fit. The household has three levers: raise the saving, lower a target, or move a date. Moving the house deposit from eight years to nine lowers its monthly saving from $469 to $410, and the total to $980, which fits. The emergency fund stays first because it protects the others, as the earlier lesson showed. The point is that a goal is a trade-off. Giving a date to each goal shows which one has to give.
When the return is not certain
A savings account pays a known rate, so the saving needed is exact. An investment in shares does not pay a known rate. In the lesson on risk and return the S&P 500 fell 36.55% in 2008 and rose 32.15% in 2013. A goal with a date is hurt by a bad stretch just before the date, because there is no time to recover.
One way to test a plan is to replay history. Take every run of N consecutive years in the data, and ask what would have happened if the household had saved the same amount each year and earned each run’s actual returns. Each run is a window. The share of windows that reached the goal is a fact about the past. It is not the probability of reaching the goal in future, because the windows overlap heavily and come from only 25 years. It does show how wide the range of outcomes was.
This is a decision under uncertainty: the outcomes are not known in advance, and the choice has to be judged by more than the average. Three things are worth looking at. The median window shows a typical result. The worst window shows what a bad run does. And the count of windows that reached the goal shows how often the plan worked. A choice with a higher median can still have a worse worst case.
Test a goal against history
Set the goal, the number of years until it is due, and the monthly saving. The calculator replays every window of that length from 2000 to 2024, saving the same amount each year and earning the S&P 500’s actual annual return, and counts the windows that reached the goal. It also shows the worst, median and best ending balances, and compares them with a savings account paying 3%.
Saving $700 a month for 5 years toward $50,000, stocks reached the goal in 13 of the 21 windows of 5 years from 2000 to 2024, which is 61.90%. The worst window ended at $32,664 and the best at $64,643. A savings account paying 3% ends at $44,597, which is $5,403 short, and reaching the goal with it would take $785 a month. Stocks ended ahead of the account in 90.48% of the windows.
Four experiments. First, leave the starting settings alone. Saving $700 a month for five years toward $50,000, stocks reached the goal in 13 of 21 windows, 61.90%. The worst window ended at $32,664 and the best at $64,643, with a median of $52,391. The savings account ends at $44,597, $5,403 short, and would need $785 a month. Stocks ended ahead of the account in 90.48% of the windows, yet reached the goal in fewer. The two figures differ because the goal sits above what the account delivers, and a stock window can beat the account and still fall short of the goal. Second, set the goal to $100,000 and the years to 10. Stocks reached it in 15 of 16 windows. The worst window ended at $89,144, and the account at $96,297. A longer time gave the stocks more room to recover. Third, set the goal to $20,000, the years to 3 and the saving to $500. Stocks reached the goal in only 11 of 23 windows, 47.83%, and the account ends at $18,545. A short deadline leaves little time to recover from a bad run. Fourth, return to $50,000 and five years and raise the saving to $1,000. Stocks reached the goal in 20 of 21 windows. But in the worst window they ended at $46,664, below the goal, while the account ends at $63,710 and cannot miss. More saving makes most outcomes safe. It does not remove the bad window.
How to read the result
Several simple questions help with a decision like this. How bad is the worst window, and could the household live with it? If the goal is a fixed cost with a firm date, such as a tuition payment, a miss may be costly and the certain account has an advantage. If the date can move, the stocks’ wider range may be acceptable. How many windows were there? A 15-year window has only 11 runs in this data, so the count is thin. And would a bit more saving or a later date make the choice matter less? In the fourth experiment, raising the saving by $300 a month lifted the worst window by about $14,000. The lesson on behavioural biases adds a warning: people tend to overweight the recent past, so a good run of years can make a risky option look safer than it is.
What this lesson leaves out
- History is not a forecast. The windows come from 25 years of one market. Future returns may be better or worse, and the windows overlap, so they are not independent trials.
- Few windows for long goals. A 15-year goal has 11 windows and a 3-year goal has 23. Counts from so few runs are rough.
- An invented account rate. The 3% savings account is made up. Real rates vary with the central bank’s policy and the lender.
- All savings in one asset. The calculator puts everything into the S&P 500 or into the account. Real portfolios mix assets, as the lesson on diversification shows.
- No fees, tax or inflation. Returns are before fees and tax, and the goal is a fixed dollar amount, so its buying power is not adjusted.
- Yearly saving added at year end. Real saving happens each month, which would change the figures slightly.
- No advice. The lesson shows a way to test a plan. It does not recommend an investment or an amount.
Common mistakes
Setting a goal with no date
Without a date there is no monthly amount, and no way to tell whether the saving is enough.
Funding every goal at once
The three goals did not fit in $1,000 a month. Decide which comes first and which date moves.
Judging a choice only by its average
A higher median can come with a worse worst case. A goal with a fixed date has to survive the bad window.
Treating the share of windows as a probability
The windows overlap and come from one short period. The share describes the past range, not the odds of the future.
Taking risk for a goal that is close
The shorter the time left, the less room the money has to recover. The three-year goal reached the target in fewer than half the windows.
Try it yourself
1. A goal of $15,000 is due in four years. A savings account pays 3% and the yearly saving is added at each year end. What monthly saving is needed?
Show the working
The growth factor is (1.034 − 1) ÷ 0.03 = 4.1836. Then 15,000 ÷ (12 × 4.1836) = about $299 a month.
2. The three goals need $271, $299 and $469 a month. The household can save $1,000. By how much is the plan over?
Show the working
The total is about $1,038 a month, which is $38 more than $1,000.
3. If the house deposit moves from eight years to nine, what is the new total, and does it fit?
Show the working
The deposit then needs $410 a month. The total is $980, which fits within $1,000.
4. How many ten-year windows are there in the annual returns for 2000 to 2024?
Show the working
There are 25 years of data, so the windows start in 2000 through 2015: 25 − 10 + 1 = 16.
5. At $700 a month for five years, stocks reached $50,000 in 13 of 21 windows. What share is that, and why is it not a probability?
Show the working
13 ÷ 21 = 61.90%. The windows overlap and come from only 25 years of one market, so the share describes what happened, not what will.
Where this is used
- A household turns each goal into a monthly amount and checks that the total fits its budget.
- A planner replays historical returns to show a client the range of outcomes for a goal.
- A company runs scenarios on its forecasts, as in the lesson on sensitivity and scenario analysis.
- An investor judges a choice by its worst case and its median as well as its average.
- A lender or adviser asks how firm a date is before suggesting how risky the saving can be.
Key terms
- Financial goal
- A target amount to be reached by a date.
- Monthly saving
- The amount set aside each month to reach a goal.
- Priority
- The order in which goals are funded when money is limited.
- Uncertainty
- Not knowing in advance what an outcome will be.
- Window
- A run of consecutive years taken from historical data.
- Median
- The middle outcome, with half of the outcomes above and half below.
- Worst case
- The poorest outcome among those tested.
- Shortfall
- The amount by which an outcome falls short of the goal.
- Time horizon
- The length of time until the money is needed.
Questions people ask
What makes a financial goal useful?
An amount, a date, a monthly saving that follows from them, and a priority against other goals.
Why does a shorter goal make stocks riskier?
Because there is less time to recover from a bad run. In the calculator the three-year goal reached its target in fewer than half the windows.
Does the share of windows tell me my chance of success?
No. It describes what happened in history. The windows overlap and the data cover only 25 years.
Is a certain account always better for a goal?
Not always. It cannot miss the rate, but it may need a larger monthly saving. Which is better depends on how firm the date is and what a miss would cost.
Sources and review
- Aswath Damodaran, NYU Stern, Historical returns on stocks, bonds and bills: 1928-2024 (last updated 5 January 2026), for the annual returns of the S&P 500 including dividends and of the 10-year US Treasury bond for 2000 to 2024. The page names its data source as multiple data services.
- Aswath Damodaran, NYU Stern, Annual returns on stock, T.bonds and T.bills: 1928 - current (last updated 5 January 2019), an older edition of the same dataset, used to check the 2000 to 2018 values.
How the numbers were checked: the monthly savings needed, the window counts, the worst, median and best balances and the four experiments were recomputed in plain code from the annual returns, and the calculator, which runs separately, was compared with that code for every combination of settings it allows. The annual returns are the 2000 to 2024 values used in the lesson on risk and return, checked there against two editions of the source. The household and the savings account rate are invented.