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?

Question

Mathematics

Elena Reynolds

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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Tatiana · Answer 1

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.