gamesblog

Interest and doubling

Simple against compound interest, the rule of 72 beside the exact doubling time, and what 12% compounded monthly really pays in a year.

  • Money
  • Untimed
  • Endless levels

How it plays

Each question is money left to grow: simple interest, compound interest, the gap between them, how long until it doubles or triples, the rate that turned one sum into another, and the effective rate behind a nominal one.

Every prompt states its convention — yearly compounding unless it says otherwise — and its rounding. The rule of 72 is asked as a rule, and the exact time is asked as exact; the working always shows both, and how far apart they are.

The wrong options are the real slips: simple interest where it compounds, the amount given for the interest, the nominal rate taken as the effective one, 100 ÷ r for the doubling time. The rates are illustrative; the money is in the currency you pick.

Keys

Space starts and skips ahead · 1–9 pick · Enter submits · Esc stops. On a phone, tap.

What it trains

This makes interest, compounding and doubling-time questions of these kinds quicker and surer. It is not financial advice and claims nothing wider.

Learn

How to get better at interest and doubling: the method, the techniques, what each new level asks of you, and the traps the wrong answers are made of.

Your approach to each question

  1. Read the convention: simple or compound, and how often it compounds. Yearly is the default; half-yearly, quarterly and monthly are always said.
  2. Read what is asked: the interest alone, or the total paid back. Many wrong options are the right sum answering the other question.
  3. For a doubling time, read whether it wants the rule of 72 or the exact answer. They are different questions with different right answers.
  4. Estimate before you choose: simple interest is always the smaller, and compounding’s extra is small over a few years at low rates and large over many years at high ones.

Techniques and tricks

  • Simple interest in one line

    Interest = principal × rate × years ÷ 100, on the original sum only. The total paid back adds the principal.

    e.g. ₹5,000 at 6% for 4 years: 5,000 × 6 × 4 ÷ 100 = ₹1,200, so ₹6,200 in all.

  • Compound year by year

    For two or three years, multiply by 1 + r one year at a time. Each year’s interest is on the new total.

    e.g. ₹5,000 at 10% for 3 years: 5,500, 6,050, 6,655, so ₹1,655 of interest.

  • Two years: the gap is P × r²

    Over two years, compound pays the same as simple plus interest on the first year’s interest: principal × rate².

    e.g. ₹10,000 at 10%: 10,000 × 0.1 × 0.1 = ₹100 more.

  • The rule of 72

    Money at r% a year doubles in about 72 ÷ r years. It is close to exact near 8%, a little long at low rates and short at high ones.

    e.g. 8%: 72 ÷ 8 = 9 years; exactly 9.01.

  • Exact doubling without logs

    The exact doubling time is very close to 69.3 ÷ r + 0.35 years. For tripling, use 109.9 ÷ r + 0.55.

    e.g. 10%: 6.93 + 0.35 = 7.28, against an exact 7.27. Tripling at 10%: 10.99 + 0.55 = 11.54, against 11.53.

  • Effective rate: compound the periods

    Divide the yearly rate by the number of periods, add 1, raise to that many periods, take 1 away. Half-yearly is just a square.

    e.g. 10% half-yearly: 1.05² = 1.1025, so 10.25%. 12% monthly: 1.01¹² = 1.1268, so 12.68%.

  • Two-year rate by a square root

    If a sum grows by a ratio over 2 years, the yearly factor is the square root of that ratio.

    e.g. ₹1,600 to ₹2,304: ratio 1.44, √1.44 = 1.2, so 20%.

As the levels climb

  • The kinds unlock in pairs: simple interest and the rule of 72 at level 0; compound interest and compound minus simple at level 1; exact doubling and the effective rate at level 3; finding the rate at level 5.
  • Between unlocks, and for ever after, the sums grow and the horizons and rates stretch. From size 3 the rule of 72 uses any rate, not just the ones 72 divides, so expect answers like 72 ÷ 7 = 10.3.
  • From the same point, some exact questions ask when money triples, not doubles. Switch to the tripling version of the formula, and do not just multiply the doubling time by 1.5.
  • Bigger sums give a little more time, 8% more per notch for the first twelve. Spend it on the estimate that catches a simple-interest answer.

Traps to avoid

  • Simple interest where it compounds, or compound where it is simple. Simple is always the smaller over more than a year; check which the question says.
  • The amount given for the interest, or the interest for the amount. Re-read the last words of the question.
  • The nominal rate taken as the effective one. Compounding more often always pays a little more than the nominal rate.
  • 100 ÷ r for a doubling time. That is how long simple interest takes; compounding gets there sooner.
  • Halving the total growth to find a two-year rate: 44% over two years is not 22% a year, because the second year earns interest on the first.

How to practise

  • Use “Kinds of question” to practise the doubling and effective-rate kinds on their own until the shortcuts are automatic.
  • Switch Answer by to “Typing the answer”; amounts count within 1 of your currency and doubling times within 0.1 of a year, so you must actually finish.
  • Pick your own Currency: the arithmetic does not change, but sums in money you use are easier to sense the size of.

Levels

It is untimed unless you turn the clock on. There is no last level: at least one dial turns without end. Your level is judged on your last ten answers, every ten: 90% moves you up, below 80% moves you down, which holds most people near four in five right.

All of it is in the settings beside Start — how many answers a judgement looks at and how often it recalibrates, the thresholds, the time, which questions, how many options, and whether you see each verdict at once or review them together at the judgement. You can also jump to any level.

More money

All games →