Version 2026.2 | Reviewed 2026-09-09
General US-focused education. No individualized financial, investment, tax, or legal advice. Investing can result in loss.
Work offline or print this page. Entries in this HTML workbook are not saved; copy or print them before leaving. Use fictional data.
A positive monthly budget can still contain a week when cash runs short.
Illustration: You start week 1 with $300. A $1,200 bill is due before a $1,500 paycheck arrives in week 2. The two-week total is positive, but week 1 has a $900 timing gap. A plan must address the due date or available cash; a positive final total does not remove that gap.
| Period | Starting cash | Income | Expenses | Ending cash |
|---|---|---|---|---|
| Week 1 | $300 | $0 | $1,200 | −$900 |
| Week 2 | −$900 | $1,500 | $0 | $600 |
You start with $500, receive $800, and pay $950 in week 1. In week 2, you receive $0 and pay $400. Calculate both ending balances and identify the first shortfall.
Week 1 ends at $350. Week 2 ends at −$50. The first shortfall occurs in week 2.
A reserve is money set aside for an unexpected expense; access is part of its purpose.
Illustration: A person models $1,800 of essential monthly spending and chooses to explore a three-month reserve scenario. The scenario target is $5,400. With $2,400 already saved, the gap is $3,000. Saving $250 monthly would close that gap in 12 months, assuming no withdrawals or interest. Three months is an example input, not a recommendation.
| Input | Example |
|---|---|
| Essential spending | $1,800/month |
| Scenario duration | 3 months |
| Scenario target | $5,400 |
| Current reserve | $2,400 |
| Remaining gap | $3,000 |
Model $2,000 in essential spending for two months. Starting reserves are $1,000 and monthly additions are $300. How long does the $3,000 gap take to close?
10 months, with no interest, withdrawals, or changes in spending.
A goal needs an amount, a date, and a way to handle uncertainty.
Illustration: Goal A is a $2,400 payment due in six months. Goal B is a flexible project planned several years away. Both involve saving, but Goal A has a tighter deadline and less room to recover from a fall in value. With no starting balance or interest, Goal A requires $400 per month.
| Question | Goal A | Goal B |
|---|---|---|
| Amount | $2,400 | Still being estimated |
| Deadline | 6 months | Several years |
| Flexibility | Low | Higher |
| Key uncertainty | Cash available on the date | Final cost and timing |
A $3,600 goal is due in nine months. You have $900 set aside. Ignoring interest, how much remains and what equal monthly amount closes the gap?
$2,700 remains. Nine equal monthly amounts of $300 close the gap.
Simple interest applies the rate to the original principal, without interest on prior interest.
Original arithmetic example: $1,000 at a hypothetical 5% annual simple rate for three years earns $1,000 × 0.05 × 3 = $150. The ending amount is $1,150. Each year adds $50 because the calculation always uses the original $1,000.
| Year | Interest this year | Total balance |
|---|---|---|
| 0 | $0 | $1,000 |
| 1 | $50 | $1,050 |
| 2 | $50 | $1,100 |
| 3 | $50 | $1,150 |
Calculate simple interest on $2,000 at 6% annually for 18 months. Convert the time to years before multiplying.
18 months = 1.5 years. Interest = $2,000 × 0.06 × 1.5 = $180. Ending amount = $2,180.
Compound interest adds earlier interest to the base that earns the next period’s interest.
Original arithmetic example: Begin with $1,000 at 10% annually, compounded once per year. Year 1 adds $100, reaching $1,100. Year 2 adds $110, reaching $1,210. The extra $10 compared with simple interest is interest earned on the first year’s $100.
| Year | Opening amount | Interest | Ending amount |
|---|---|---|---|
| 1 | $1,000 | $100 | $1,100 |
| 2 | $1,100 | $110 | $1,210 |
Start with $2,000 at a hypothetical 5% annual rate for two years, compounded annually, with no contributions. Calculate each year separately.
Year 1: $2,100. Year 2: $2,205. Total growth: $205. Simple interest would have produced $2,200.
A larger number of dollars does not always buy more goods and services.
Original arithmetic example: An item costs $100 today and rises 5% to $105 in one year. A fixed $100 can buy 100/105 = 95.24% of the original quantity. Separately, a 7% nominal return with 3% inflation gives 1.07/1.03 − 1 = approximately 3.88% real return.
| Measure | Illustration |
|---|---|
| Future nominal amount | $100 |
| One-year inflation assumption | 5% |
| Today’s purchasing power | $95.24 |
| Reduction in purchasing power | $4.76 |
A future $1,210 will be received in two years. At a constant 10% annual inflation assumption, what is its value in today’s purchasing power?
$1,210 / 1.10² = $1,000 in today’s purchasing power.
Different labels do not necessarily mean different underlying risks.
Original illustration: A $10,000 example portfolio puts $5,000 into company A and $5,000 into company B. If A falls 40% while B is unchanged, the total falls $2,000, or 20%. A portfolio wholly in A would lose 40%. If both companies fall 40%, splitting the money between them does not help in this scenario.
| Scenario | Company A | Company B | Portfolio change |
|---|---|---|---|
| A falls; B unchanged | −40% | 0% | −20% |
| Both fall together | −40% | −40% | −40% |
An example portfolio is 25% in A and 75% in B. A loses 20% and B is unchanged. What is the portfolio change, ignoring fees and rebalancing?
0.25 × −20% + 0.75 × 0% = −5%.
A recurring fee reduces both today’s balance and the amount left to grow.
Original arithmetic example: Start with $10,000, assume a 5% gross annual return, and apply a 1% annual fee after growth. After one year, $10,000 × 1.05 × 0.99 = $10,395, compared with $10,500 without that fee. After two years the fee scenario is $10,805.60, versus $11,025. The $219.40 difference includes fees and the growth those deducted dollars no longer earn.
| Year | Without fee | With 1% fee |
|---|---|---|
| 0 | $10,000 | $10,000 |
| 1 | $10,500 | $10,395 |
| 2 | $11,025 | $10,805.60 |
Starting with $1,000 and zero gross return, apply a 1% fee after each year for two years. What remains?
$1,000 × 0.99² = $980.10. The total reduction is $19.90.
Prevention and prompt detection work together.
Practice scenario: A notice says a new withdrawal destination was added. You did not make the change. Open the provider’s known app or type its known address, review the activity, and contact the institution through a verified channel. Do not use a phone number from the unexpected notice to establish its legitimacy.
| Control | What to check |
|---|---|
| Unique password | Not reused on another service |
| Multifactor authentication | Enabled through the provider |
| Alerts | Changes and transactions monitored |
| Recovery email | Secured and accessible |
| Review routine | Statements and access activity checked |
Make a security checklist for a fictional account. Include one preventive control, one detection control, and one independently verified contact method. Do not record a real password.
One valid answer: unique password with multifactor authentication; alerts for account changes; the contact number from the provider’s known website.
Verify the sender through a channel you already trust.
Practice scenario: A text says, “Your brokerage is locked. Verify your login now.” It links to an unfamiliar domain and creates urgency. Instead of using that link, open the brokerage app directly. If there is no matching notice, contact the broker through the app’s verified support channel. The message itself should not supply the only evidence that it is legitimate.
| Message cue | Verification step |
|---|---|
| Unexpected urgency | Pause and inspect |
| Login link | Open the known app independently |
| Request for a code | Do not disclose it to the sender |
| Payment instructions | Confirm through a verified contact |
Write the first three actions you would take after an unexpected password-reset text. Use fictional details only.
A valid sequence: do not click the link; open the known account app independently; inspect activity and contact verified support if needed.