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Joel has a vintage comic book worth $\$360$ . According to a dealer, the value of this particular comic book will increase by $5\%$ each year. How much will the comic book be worth in $15$ years? $\newline$ If necessary, round your answer to the nearest cent. $\newline$ $\$$ ____

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Exponential growth and decay: word problems

Full solution

Q. Joel has a vintage comic book worth

\$360

. According to a dealer, the value of this particular comic book will increase by

5\%

each year. How much will the comic book be worth in

15

years?

\newline

If necessary, round your answer to the nearest cent.

\newline

\$

____

Identify Value and Increase: Identify the initial value of the comic book and the annual percentage increase. $\newline$ The initial value of the comic book, $P$ , is $\$360$ . $\newline$ The annual percentage increase, $r$ , is $5\%$ .
Convert Percentage to Decimal: Convert the percentage increase to a decimal to use in calculations. $\newline$ To convert a percentage to a decimal, divide by $100$ . $\newline$ $r = 5\% = \frac{5}{100} = 0.05$
Determine Number of Years: Determine the number of years the comic book will appreciate in value. The number of years, $t$ , is $15$ .
Use Compound Interest Formula: Use the formula for compound interest to calculate the future value of the comic book. $\newline$ The formula for compound interest is $A = P(1 + r)^t$ , where $A$ is the amount of money accumulated after $n$ years, including interest.
Substitute Values and Calculate: Substitute the known values into the formula and calculate the future value. $A = 360(1 + 0.05)^{15}$
Calculate Future Value: Calculate the future value using the values from Step $5$ . $\newline$ $A = 360(1.05)^{15}$ $\newline$ $A \approx 360(2.07893)$ (using a calculator for $1.05$ to the power of $15$ ) $\newline$ $A \approx 748.4078$
Round to Nearest Cent: Round the answer to the nearest cent, if necessary. $\newline$ The future value of the comic book rounded to the nearest cent is approximately $\$748.41$ .

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