Practice: How Investing Works
Eleven scored problems on growth, inflation, risk, and your own behavior, with worked answers, plus a short plan to write for yourself.
What you'll do
This set puts the first module to work. You'll calculate how money grows, what inflation does to it, and what it takes to recover from a loss. You'll sort examples into saving, investing, and speculating, tell risk tolerance from risk capacity, and spot four common behavior patterns. Each answer comes with the working, and your score appears as you go. Nothing is recorded outside this browser. A calculator helps.
This draws on
Work through the problems in order. Check each answer when you've committed to it: the score counts your first try. Every number here is hypothetical, and none of it is a forecast or a recommendation.
Growth and inflation
1. You invest $5,000 and it earns 6% a year for two years, with the first year's gain left invested. What's it worth at the end?
$5,000 × 1.06 = $5,300 after one year, and $5,300 × 1.06 = $5,618 after two. The second year earns $318, not $300, because it also earns 6% on the first year's $300. Review: Compounding.
2. Using the Rule of 72, about how many years does money take to double at 8% a year?
72 ÷ 8 = 9 years. The rule is an approximation, and here it's almost exact: $1 growing at 8% for 9 years becomes $2.00. Review: Compounding.
3. Ana invests $10,000 at 6% a year for 30 years. Ben invests $10,000 at the same rate for 20 years. How many times larger is Ana's ending amount than Ben's? Give two decimal places.
Ana's extra ten years multiply her money by 1.06 ten more times: 1.0610 = 1.79. She ends with $57,435 and Ben with $32,071. Half as long again produced 79% more money, because the last ten years grew the largest balance. Review: Compounding.
4. A week's groceries cost $100 today. If prices rise 3% a year, what will the same groceries cost in 10 years?
$100 × 1.0310 = $134.39. Inflation compounds in the same way returns do, working against you. Review: Inflation and Purchasing Power.
5. A savings account pays 2% a year while prices rise 3% a year. Roughly what's the real return, to the nearest whole percent? Use a minus sign if it's negative.
About −1%. The balance grows 2% and what it buys shrinks 3%, so its purchasing power falls by about 1% a year. The exact figure is 1.02 ÷ 1.03 − 1 = −0.97%. The account never shows a loss, and the money still buys less each year. Review: Inflation and Purchasing Power.
Risk
6. An investment falls 20%. What percentage gain does it need to get back to where it started?
25%. $100 falls to $80, and getting back to $100 takes a $20 gain on $80: $20 ÷ $80 = 25%. The gain needed is always bigger than the loss, because it's measured from a smaller amount. Review: Risk and Return.
7. Two investments both average 5% a year. The first returns exactly 5% every year. The second alternates between +25% and −15%. Which is worth more after 10 years?
$10,000 at a steady 5% becomes $16,289. With the swings, each pair of years multiplies the money by 1.25 × 0.85 = 1.0625, and five pairs give $13,541. Same average, about $2,750 less. Review: Risk and Return.
8. Put these in order from the narrowest range of yearly results to the widest.
- A fund holding hundreds of stocks
- The stock of one company
- An insured savings account
- A fund holding many bonds
Savings account, bond fund, stock fund, single stock. The wider the range of possible results, the higher the return investors expect for holding it, and the more a bad year can hurt. A fund of many stocks swings less than one stock because its holdings don't all fall at once. Review: Risk and Return.
9. Is each of these saving, investing, or speculating?
- Keeping next year's rent in an insured savings account
- Buying a fund of many stocks to hold for 25 years
- Buying a stock that's all over social media, hoping to sell it next week
- Buying a bond to collect its interest until it's repaid
- Holding three months of expenses in cash for emergencies
Saving keeps money safe and available for a known, near need. Investing buys something expected to produce a return over years, accepting that its price will move. Speculating is a bet on a short-term price change, with no view on what the thing is worth. Review: What Is Investing?.
You
10. Which idea does each statement describe?
- Dana needs this money for a house deposit in two years
- Lee couldn't sleep when her account fell 10%
- Sam has a steady income and no debts, so a loss wouldn't change his plans
- Pat is 30 and investing for retirement at 65
- Ravi would have to sell if he lost his job, because this is all he has
Time horizon is when the money is needed. Risk tolerance is how much of a fall you can live through without abandoning your plan. Risk capacity is how much of a fall your finances can absorb. They can point in different directions: Sam can afford risk whether or not he likes it, and Ravi can't afford it however calm he feels. Review: Time Horizon and Risk Tolerance.
11. Which pattern is at work in each case?
- After three good years, Maya assumes the market will keep rising like this
- Tom refuses to sell a losing stock because selling would make the loss feel real
- Jo buys a stock after hearing how much a coworker made on it
- Everyone Ali knows is selling, so he sells too, without a reason of his own
Recency bias treats the recent past as permanent. Loss aversion makes a loss hurt more than an equal gain pleases, which distorts decisions about losing positions. Fear of missing out is the pull of other people's gains. Herd behavior is doing what the crowd does because the crowd is doing it. Naming the pattern is the first step to not acting on it. Review: Your Own Behavior Is Part of the Risk.
Your own plan
12. In a few lines, write down what one pot of your own money is for, when you'll need it, and what you intend to do if it's down 30% a year from now. This isn't scored.
What a useful answer includes
A purpose and a date, which give you the time horizon. An honest view of whether you could leave the money alone through a 30% fall, which is your tolerance, and whether you could afford to, which is your capacity. And a decision made now about what you'll do then, such as "nothing, and I won't check more than once a month". A plan written while calm is the one from Your Own Behavior Is Part of the Risk.