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25 February, 20:12

The value of good wine increases with age. Thus, if you are a wine dealer, you have the problem of deciding whether to sell your wine now, at a price of $P a bottle, or to sell it later at a higher price. Suppose you know that the amount a wine-drinker is willing to pay for a bottle of this wine t years from now is $P (1 + 20). Assuming continuous compounding and a prevailing interest rate of 5% per year, when is the best time to sell your wine?

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  1. 25 February, 21:26
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    Answer: 64 years

    Step-by-step explanation:

    Let assume the dealer sold the bottle now for $P, then invested that money at 5% interest. The return would be:

    R1 = P (1.05) ^t,

    This means that after t years, the dealer would have the total amount of:

    $P*1.05^t.

    If the dealer prefer to wait for t years from now to sell the bottle of wine, then he will get the return of:

    R2 = $P (1 + 20).

    The value of t which will make both returns equal, will be;

    R1 = R2.

    P*1.05^t = P (1+20)

    P will cancel out

    1.05^t = 21

    Log both sides

    Log1.05^t = Log21

    tLog1.05 = Log21

    t = Log21/Log1.05

    t = 64 years

    The best time to sell the wine is therefore 64years from now.
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