Question
collector of rare books has a first-edition book worth $262, which he anticipates will grow in value at a rate of 15% per year. How much will this book be worth 10 years from now?
If necessary, round your answer to the nearest cent.
If necessary, round your answer to the nearest cent.
Answers
GPT-4o mini
To calculate the future value of a book (or any investment) growing at a specific rate, we can use the formula for compound interest:
\[
FV = P(1 + r)^t
\]
Where:
- \( FV \) = future value
- \( P \) = present value (initial amount)
- \( r \) = annual growth rate (as a decimal)
- \( t \) = number of years
In this case:
- \( P = 262 \)
- \( r = 0.15 \) (15% as a decimal)
- \( t = 10 \)
Now, plug the values into the formula:
\[
FV = 262(1 + 0.15)^{10}
\]
First, calculate \( (1 + 0.15)^{10} \):
\[
(1.15)^{10} \approx 4.045557
\]
Now, multiply this by the present value:
\[
FV \approx 262 \times 4.045557 \approx 1064.497
\]
Rounding to the nearest cent, the future value of the book will be approximately:
\[
\text{FV} \approx 1064.50
\]
Therefore, the book will be worth approximately **$1,064.50** in 10 years.
\[
FV = P(1 + r)^t
\]
Where:
- \( FV \) = future value
- \( P \) = present value (initial amount)
- \( r \) = annual growth rate (as a decimal)
- \( t \) = number of years
In this case:
- \( P = 262 \)
- \( r = 0.15 \) (15% as a decimal)
- \( t = 10 \)
Now, plug the values into the formula:
\[
FV = 262(1 + 0.15)^{10}
\]
First, calculate \( (1 + 0.15)^{10} \):
\[
(1.15)^{10} \approx 4.045557
\]
Now, multiply this by the present value:
\[
FV \approx 262 \times 4.045557 \approx 1064.497
\]
Rounding to the nearest cent, the future value of the book will be approximately:
\[
\text{FV} \approx 1064.50
\]
Therefore, the book will be worth approximately **$1,064.50** in 10 years.