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Present value

What ₹1,00,000 in five years is worth today, real against nominal returns, a stream of payments and a project's NPV — money moved through time.

  • Money
  • Untimed
  • Endless levels

How it plays

Each question moves money through time: grow a sum forward, discount a promise back to today, strip inflation out of a return, value a run of yearly payments or one that goes on for ever, or net a project's cost against what it pays.

Every prompt fixes the convention — yearly compounding, cash at the end of each year — and the rounding. Options are at least 3% apart; a typed answer counts within 0.5%. New kinds unlock as you climb, and the sums and horizons grow without end.

The wrong options are the real slips: simple interest where it compounds, nominal minus inflation for the real rate, one year too few, a stream valued at its plain total. 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 present-value and inflation arithmetic of these kinds quicker and surer. It is not financial advice and claims nothing wider.

Learn

How to get better at present value: 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. Decide which way the money moves. Forward in time, multiply by (1 + r) once for each year; back to today, divide by it.
  2. Count the years carefully. Cash comes at the end of each year, so a payment “in 5 years” is divided by (1 + r) five times, and the first of a run of yearly payments waits one year.
  3. For a run of payments, use the formula for the whole run rather than discounting each one, unless there are only two or three.
  4. Check the size before you choose: money today is always worth less than the same sum later, and a stream is always worth less today than its plain total.

Techniques and tricks

  • Powers by squaring

    Build (1 + r)ⁿ by squaring: square for 2 years, again for 4, again for 8, and multiply in the odd years.

    e.g. 1.05² = 1.1025, 1.05⁴ = 1.2155, 1.05⁸ = 1.4775.

  • Rule of 72 as a check

    At r%, money doubles in about 72 ÷ r years. Use it to check the size of a future value, or the present value of a sum that far away (about half).

    e.g. 20,000 at 8% for 9 years is about 40,000; exactly 39,980.

  • Real rate by division

    The real rate is (1 + nominal) ÷ (1 + inflation) − 1. It is a little less than nominal minus inflation.

    e.g. 10% with 4% inflation: 1.10 ÷ 1.04 = 1.0577, so 5.77%, not 6%.

  • A stream’s value today

    Payments of c at the end of each year for n years are worth c × (1 − (1 + r)⁻ⁿ) ÷ r today. Saved instead, they grow to c × ((1 + r)ⁿ − 1) ÷ r by the last payment.

    e.g. 10,000 a year for 3 years at 10%: worth 24,869 today; saved, 33,100 after the last payment.

  • For ever is payment ÷ rate

    A payment c every year for ever is worth c ÷ r today, with r as a decimal: a sum that throws off r of itself each year without shrinking.

    e.g. 3,000 a year at 5%: 3,000 ÷ 0.05 = 60,000.

  • NPV: discount, add, subtract the cost

    Divide each year’s payment by (1 + r) for each year it waits, add them, and take away today’s cost. Positive means the project beats leaving the money at r.

    e.g. Cost 9,000, then 5,000 and 6,000 at 10%: 4,545 + 4,959 − 9,000 = +504.

  • Now or later: move one to the other

    Either discount the later sum to today, or grow today’s sum to the later date, and compare like with like.

    e.g. At 8%, 50,000 in 3 years is worth 39,692 today, so 40,000 now is worth more.

As the levels climb

  • The kinds unlock in this order: future and present value at level 0; real against nominal and inflation over years at level 1; saving every year, a stream of payments and a payment for ever at level 3; net present value and now or later at level 5.
  • Between unlocks, and for ever after, the sums grow and the horizons lengthen, up to 40 years. Long horizons are where squaring pays; multiplying 30 times by hand is where slips come from.
  • At the stream kinds, decide first whether the question wants today’s value or the value after the last payment. The two formulas look alike and give very different answers.
  • Bigger sums give a little more time, 8% more per notch for the first twelve. Spend it on the size check: options are at least 3% apart, so a rough answer often decides.

Traps to avoid

  • Simple interest where it compounds: multiplying by 1 + n × r instead of (1 + r)ⁿ. Over many years it is far too small going forward, and dividing back by 1 + n × r leaves too much.
  • One year too few: dividing or multiplying by (1 + r) once less than the years. Count the years against the payments.
  • Nominal minus inflation given as the real rate. It is close, but options can be close too; divide instead.
  • A stream valued at its plain total, c × n, or that total discounted all from the last year. Each payment waits a different time.
  • For a payment for ever, dividing by the rate as a whole number, 3,000 ÷ 5, instead of 3,000 ÷ 0.05.

How to practise

  • Use “Kinds of question” to drill future and present value until squaring the factor is quick; every later kind is built from them.
  • Switch Answer by to “Typing the answer”: a typed amount counts within 0.5%, so a growth factor rounded to four decimal places is plenty.
  • Pick your own Currency; with ₹ the sums are in tens of thousands and up, as real savings are.

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.

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