Final answer:
The future value of a painting valued at $10,000 with a 3% annual increase over 5 years can be found using the compound interest formula, resulting in a value of approximately $11,592.74 after 5 years.
Step-by-step explanation:
The student is asking about the future value of an investment with compound interest. In this case, a painting that increases in value at a rate of 3% per year. To calculate the future value of the painting after 5 years, we can use the compound interest formula:
FV = P × (1 + r)^n, where:
- FV is the future value of the investment,
- P 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.
Using the information provided for the painting valued at $10,000 with a 3% annual increase, the formula will look like this:
$10,000 × (1 + 0.03)^5 = $11,592.74
The painting will be worth approximately $11,592.74 after 5 years.