8. Around 1890 the vineyards in Bordeaux were infected by Phylloxera, a louse that attacks the vine’s roots. To preserve the original grape varieties, the Bordeaux vines were grafted onto roots taken from American grape plants. Since 1890 all Bordeaux wines have been made with vines grafted onto American roots. These wines do not taste the same as the wines made before the Phylloxera infection. A bottle of Bordeaux wine that was made before the infection sells for thousands of dollars. Suppose you had a bottle of pre-Phylloxera Bordeaux that you could sell today for $2000 and you were interested only in its value as an investment. To make it worthwhile for you to hold on to your investment, what must be the expected price of the bottle in n years if the market rate of interest is i?