Problem

APPLICATION
5. A signed Miguel Cabrera baseball glove is worth $\$ 1000$. Its value increases by $15 \%$ each year. How much is the glove going to be worth in 10 years from now? [ /3]

Answer

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Answer

Final Answer: The glove is going to be worth approximately \(\boxed{4045.56}\) in 10 years from now.

Steps

Step 1 :The problem is asking for the future value of an investment with an annual interest rate of 15%. The formula for future value is: \(FV = PV * (1 + r)^n\) where: \(FV\) is the future value of the investment, \(PV\) is the present value of the investment, \(r\) is the annual interest rate (expressed as a decimal), \(n\) is the number of years the money is invested for.

Step 2 :In this case, the present value (\(PV\)) is $1000, the annual interest rate (\(r\)) is 15% or 0.15, and the number of years (\(n\)) is 10.

Step 3 :Substitute the given values into the formula: \(FV = 1000 * (1 + 0.15)^{10}\)

Step 4 :Solving the equation gives the future value of the glove as approximately $4045.56.

Step 5 :Final Answer: The glove is going to be worth approximately \(\boxed{4045.56}\) in 10 years from now.

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