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Compound Sprint

Section: InvestingDifficulty: BasicRound length: 3–10 minFreeNo sign-up
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Complete game guide

A round of about five minutes on the one piece of arithmetic almost everyone under-reads: what an amount turns into when each year's interest joins the balance. Nine cards arrive one at a time — a one-off amount left alone, a payment made every year, a start put off by a decade, a fee taken annually, three paying-in plans racing to the same finish line. You plant a flag before the snowball rolls, and then it rolls. Within 8% is a hit, within 20% is half credit, and a miss costs one of three chances. Every rate on every card is hypothetical and stated as such, and you never type a figure of your own.

The goal

Nine cards in three stages of three, getting harder as they go. Five kinds appear: the finish value of a one-off amount; the total after paying in at the start of every year; what share is lost by starting some years late; what share a yearly fee takes over decades; and a three-lane race in which you pick the plan that finishes furthest. Every card's three slots name the condition that card turns on — the amount, the yearly payment, the years started late or the yearly fee — followed by the hypothetical annual rate and the horizon, and every card compounds once a year — which is printed above the track, because with the frequency unstated a card would have several correct answers.

Controls and play

Estimate cards take a number: tap the on-screen keypad or type, then press Enter or the plant-flag button. There is no dragging while you answer — the only slider in the game is the sandbox on the result page, and it has minus and plus buttons and left and right arrow keys that do exactly the same thing. Race cards take one of three lanes: press 1, 2 or 3, or Tab to a lane and press Enter. Text that cannot be read as a number, and a number outside the allowed range, are not answers: the button stays off and the clock keeps running. Only the clock running out marks a card wrong on your behalf.

Points and streaks

A hit — within 8% of the real finish, or within 1.5 percentage points on a share card, whichever is wider — scores full credit. Close, within 20% or 4 points, scores half and keeps your streak alive. A miss scores nothing, resets the streak and costs one of three chances. Cards are weighted 1 at the first tier, 1.3 at the second and 1.6 at the third, and the multiplier rises half a step every three non-misses up to three times. There is no speed bonus at all: paying for speed is paying for guessing. The grade runs on a weighted quality ratio out of all nine cards, so stopping early never improves it.

Finishing and results

The round ends on the ninth card or when the third chance goes. The result page puts every flag you planted against the real finish on one log scale, so you can see at a glance whether you landed behind the curve every time — the headline counts only the estimate cards you actually answered, and says separately how many you never reached. Below it: a card-by-card review, two knowledge cards that are the same in both languages, and a sandbox where an amount, a hypothetical rate and a horizon can be moved between preset steps to watch the curve respond. The sandbox scores nothing and takes no figure of yours.

Replay and progress

Every round is dealt from a seed and the share text carries it: opening that link deals the same nine cards, in the same order, with the same answers — and in either language, because the deal is language-neutral and only the sentences differ. "Play again" draws a new seed and drops the old link from the address bar. Leaving mid-round keeps the card you were on, the score, the streak, the chances and the seconds that were left, counted against that card's own limit — thirty seconds on a race card, not forty. Both clocks stop while the page is hidden.

Language and context

Both languages play the identical round: the same nine cards, the same parameters and the same answers, because nothing in the arithmetic depends on where you live. Only the unit differs — thousands of dollars in English, 万元 in Chinese — and that is a label on the input row, not a conversion. The result page's two knowledge cards are the same in both languages for the same reason. Where local rules genuinely differ, such as how often a bank applies interest, the game says that frequency is an assumption rather than teaching one market's practice as the rule.

This round covers

Interest on interest is the whole story

Simple interest adds the same amount every year; compounding adds interest to the balance, so next year's interest is charged on this year's as well. Over thirty years at a hypothetical 8%, that difference is roughly three times the finish value.

Source: SEC OIEA, How Fees and Expenses Affect Your Investment Portfolio, sec.gov

72 over the rate is the years per doubling

At a hypothetical 8% an amount doubles in about nine years, at 9% in about eight. Divide the horizon by that and you know how many doublings fit — three doublings is eight times, not six.

Source: SEC OIEA, How Fees and Expenses Affect Your Investment Portfolio, sec.gov

Most people under-read growth, badly

Asked what regular saving turns into over forty years, a clear majority of one well-known study's participants answered below a tenth of the arithmetic answer, and handing them a calculator changed almost nothing. The gap is in the reading, not the arithmetic.

Source: McKenzie & Liersch, Misunderstanding Savings Growth, Journal of Marketing Research 2011

Starting late costs doublings, not years

Putting a start off by ten years at a hypothetical 7% does not cost ten years out of forty — it costs the LAST doubling, which is the biggest one. That is why the share lost is so much larger than the share of time given up.

Source: SEC OIEA, How Fees and Expenses Affect Your Investment Portfolio, sec.gov

A 1% yearly fee is not a 1% cost

The SEC's own worked example: 100,000 at a hypothetical 4% for twenty years finishes about 208,000 with a 0.25% yearly fee and about 180,000 with a 1.00% one — a gap of roughly 28,000, because the fee comes out of the compounding base every year.

Source: SEC OIEA, How Fees and Expenses Affect Your Investment Portfolio, sec.gov

How often interest is applied changes the answer

The same stated annual rate pays more applied monthly than yearly, which is exactly why disclosure rules define an annual percentage yield that reflects the compounding frequency. Every card in this game applies it once a year and says so.

Source: CFPB, Regulation DD 12 CFR 1030.2, consumerfinance.gov

Questions people ask

How do you estimate compound growth in your head?

Divide 72 by the annual rate to get the years one doubling takes — 72 over 8 is nine years. Divide the horizon by that to get how many doublings fit: twenty-seven years at 8% is three doublings, so the amount finishes around eight times where it started. When the doublings do not come out whole, take the whole ones and add roughly a quarter of the amount for each half-doubling left over. Across the rates this game uses, that estimate lands inside its hit band on every single card — which is checked by machine before a card is ever dealt.

Why does a 1% annual fee cost so much more than 1%?

Because it is taken every year, out of the balance that would otherwise have compounded. The SEC's published example runs 100,000 at a hypothetical 4% for twenty years: with a 0.25% yearly fee it finishes near 208,000, and with a 1.00% one near 180,000 — the extra 0.75% a year costs about 28,000 over the period. The right way to estimate it is to walk the same doubling ladder on the FEE rate: 72 over 1 is 72 years to halve you, so thirty years costs roughly a quarter.

What does starting ten years late actually cost?

Far more than ten years out of forty. The years you give up are the LAST ones, when the balance is largest, so you lose a whole doubling rather than a quarter of the money. At a hypothetical 7% a ten-year delay costs about half the finish value, not a quarter. The cards in this game are sampled so that the proportional reading — a quarter of the years, a quarter of the money — always lands outside the close band.

Does paying in more always beat starting earlier?

No, and the race cards are built on exactly that. A lane that pays in for only eight years and then stops can finish ahead of one that pays in three times as much over fifteen late years, because what counts is how long each payment has to roll. Every race card in this game is checked before it is dealt: the lane that contributes the most is never the winner, and at the hardest tier neither is the lane that starts earliest.

Is this a compound interest calculator?

No. You never type a figure of your own, and you cannot compute before you commit: the flag goes down first and the snowball rolls afterwards. Every amount on screen is dealt by the game. The study behind this design found that giving people a calculator barely changed their answers, so what is on offer here is a method — the doubling ladder — and the cards are checked to make sure the method wins and the usual intuition loses.

Are the rates on the cards predictions?

No. Every rate is a hypothetical annual rate, labelled as assumed on the card and in the line above the track, and it exists so the arithmetic has a number in it. Nothing on these pages describes what any real holding has done or will do, nothing names a product, and nothing here is advice. Compounding is also fixed at once a year on every card, because leaving the frequency open would give a single card several correct answers.

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