Final answer:
Theodore's vintage painting, originally purchased for $480, is expected to increase in value by 12 percent per year. Using the compound interest formula, we calculate the future value after 15 years to determine the selling price Theodore should ask for.
Step-by-step explanation:
Theodore purchased a vintage painting worth $480, and the value is expected to increase by 12 percent per year. To find out how much Theodore should ask for the painting if he sells it in 15 years, we would use the formula for compound interest, which applies because the painting's value increases by a percentage each year. The formula is:
A = P(1 + r/n)nt
Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount ($480 in this case).
r = the annual interest rate (12%, or 0.12).
n = the number of times that interest is compounded per year (1, since the value increases annually).
t = the time the money is invested for, in years (15 years).
So, the calculation for Theodore's painting after 15 years would be:
A = 480(1 + 0.12/1)1*15
A = 480(1 + 0.12)15
A = 480(1.12)15
After calculating the above expression, the future value A that Theodore should ask for when selling the painting is found. This calculation will tell us the increased value of the painting after 15 years, reflecting the art dealer's estimate.