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  1. 032A machine turns a Rs 10 note into a Rs 20 note, but each use takes exactly one year, costs Rs 2 of electricity, and the machine breaks after 10 uses. At a 10% interest rate, what would you pay for it today?Compounding and time valueHardGoldman SachsDallas · 2026

    Try it first

    Before you discount anything: what is the machine's real net gain per use, measured at the end of the year?

    Show the worked solution

    About Rs 43. Each use ties up a Rs 10 note for a year, which at 10% costs you Rs 11 by year end, plus Rs 2 of electricity, and pays Rs 20. That is Rs 7 a year for ten years, and Rs 7 times the ten-year annuity factor of 6.1446 is Rs 43.01. If the electricity is paid at the start of each year the net is Rs 6.80 and the value Rs 41.78.

    What is one use of the machine actually worth?

    Think of lending a friend Rs 10 for a year and getting Rs 20 back. You doubled your note, but you also went a year without it, and that year had a price: whatever the money would have earned in the bank. The machine does not create Rs 10 a year; it creates Rs 20 at year end in exchange for Rs 10 today, and Rs 10 today is worth Rs 11 at year end at 10%. Take off Rs 2 of electricity and each use leaves Rs 7, received one year after you feed it the note.

    Ten uses, Rs 7 net each, discounted back to todayOne use, valued at year end:+20 out - 10 x 1.1 note in - 2 power = 7Sum of ten present valuesRs 43.01 (power paid up front: 41.78)6.36Yr 15.79Yr 25.26Yr 34.78Yr 44.35Yr 53.95Yr 63.59Yr 73.27Yr 82.97Yr 92.70Yr 10Dashed outline: Rs 7 received at the end of each year. Filled: what it is worth today at 10%.Forget the Rs 1 a year the note could have earned and you get Rs 49.16, too much.
    Each of the ten uses leaves Rs 7 at the end of its year once the Rs 11 cost of the note and the Rs 2 of electricity are taken off the Rs 20, and the ten present values fall from Rs 6.36 to Rs 2.70 and sum to Rs 43.01.
    The relationship
    PV=(20−10(1.1)−2)×1−1.1−100.10=7×6.1446=43.01PV = \big(20 - 10(1.1) - 2\big)\times\frac{1-1.1^{-10}}{0.10} = 7 \times 6.1446 = 43.01
    10(1.1)the Rs 10 note's value at year end had you kept it at 10%
    6.1446the present value of Rs 1 a year for ten years at 10%
    What it says in wordsFind the net gain of one use at the end of its year, then value ten of them as an annuity.

    Why does the timing of the electricity change the answer?

    The question does not say when you pay for power. If you pay at the end of the year, the net is the Rs 7 above. If you pay at the start, alongside the note, the Rs 2 also costs you a year of interest, Rs 2.20 by year end, and the net drops to Rs 6.80, worth Rs 41.78. State the timing assumption out loud, because an interviewer who wrote this puzzle is listening for whether you notice that cash flows need a date. The other common answer, Rs 49.16, discounts Rs 8 a year and is wrong for a reason, not a rounding: it treats the Rs 10 note as free to borrow.

    One check makes the answer believable. You could reproduce the machine with a bank loan: borrow Rs 10 at 10%, run the machine, repay Rs 11 and the Rs 2 of power, keep Rs 7. A buyer will pay up to the present value of that stream, and no more, because the bank can supply the money at 10% anyway.

    Where candidates lose it

    The usual answer is Rs 49.16: Rs 8 a year, discounted. It misses that the note fed in each year is capital with a cost. Candidates who think of each use as a project, with an outflow today and an inflow in a year, do not make this mistake.

    The second loss is giving one number with no assumption. Say when you assume the electricity is paid, give both values if asked, and the interviewer hears someone who dates every cash flow.

    What the interviewer asks next

    • What would you pay if the machine could be used once a year forever?
    • At what interest rate is the machine worth nothing?
    • If the machine could run two notes at once, what would it be worth?

    Asked at Goldman Sachs, Summer Analyst Interview, Dallas, 2026 (Wall Street Oasis): A mad scientist invents a machine that turns a standard $10 bill into a $20 bill