Question

You just purchased two coins at a price of $790 each. Because one of the coins is more collectible, you believe that its value will increase at a rate of 7.3 percent per year, while you believe the second coin will only increase at 6.7 percent per year. If you are correct, how much more will the first coin be worth in 20 years?

$100.40

Answer #1

First Coin:

Current Price = $790

Growth Rate = 7.30%

Price after 20 years = Current Price * (1 + Growth
Rate)^Period

Price after 20 years = $790 * 1.0730^20

Price after 20 years = $790 * 4.09255

Price after 20 years = $3,233.12

Second Coin:

Current Price = $790

Growth Rate = 6.70%

Price after 20 years = Current Price * (1 + Growth
Rate)^Period

Price after 20 years = $790 * 1.0670^20

Price after 20 years = $790 * 3.65838

Price after 20 years = $2,890.12

So, the first coin will worth $343.00 ($3,233.12 - $2,890.12) more than the second coin.

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