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  1. 003A pond has one lily pad on day 1. The lily pads double every day and the pond is completely covered on day 30. On what day was the pond half covered?Growth and compoundingWarm upHarris WilliamsRichmond · 2025

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    Day 29. The coverage doubles every day, so it halves when you step back one day. Full on day 30 means half on day 29, a quarter on day 28 and one thirty-second on day 25. Most of the growth in a doubling process arrives right at the end.

    Why is day 15 wrong?

    Day 15 would be right if the pond gained the same area every day, like a tank filling from a tap. Doubling is different: it is money compounding at 100% a day. Under doubling, each step back in time halves the amount, so half full is always exactly one step before full. On day 15 the pond is only one part in about 32,768 covered.

    Pond covered, last six days: each bar is double the one beforehalf the pond1/32Day 251/16Day 261/8Day 271/4Day 281/2Day 29FullDay 30the answer
    The pond is one thirty-second covered on day 25 and still only one quarter covered on day 28. It reaches half on day 29 and is full on day 30, because each day's bar is double the one before.

    Why would a banking interviewer ask this?

    It is a test of whether you think in growth rates or in straight lines. The same instinct that answers day 15 also overestimates how much of a compounding investment's value arrives early. Say that link in one sentence after you answer: it shows you know why the question is on the table.

    Where candidates lose it

    Answering day 15 is the whole trap, and many strong candidates say it because they are answering fast. The interviewer is watching whether you pause for one second and ask what kind of growth this is.

    Say day 29, then give the one-line reason: doubling forward means halving backward.

    What the interviewer asks next

    • On which day is the pond a quarter covered?
    • If you start with two lily pads, when is the pond full?
    • Where do you see this pattern in a DCF or an LBO?

    Asked at Harris Williams, Generalist, Richmond, 2025 (Wall Street Oasis): The lilypad doubles in size everyday, until the 30th day, when the pond is full