Four years ago, an art collector bought a painting for $32 500. He knows that this painting appreciates at
15% a year. What is this painting worth now, to the nearest $100?
what is
32500(1.15)^4 ?
To find out how much the painting is worth now, we need to calculate the appreciation over the past four years.
First, we need to calculate the appreciation for each year. The appreciation rate is given as 15%, which means the painting increases in value by 15% each year.
To find the appreciation for the first year, we multiply the initial value of the painting by 15% and add it to the initial value:
Appreciation for the first year = $32,500 * 15% = $32,500 * 0.15 = $4,875
To find the appreciation for the second year, we add the appreciation from the first year to the initial value and then calculate the appreciation:
Appreciation for the second year = ($32,500 + $4,875) * 15% = $37,375 * 0.15 = $5,606.25
We repeat the same process for the third and fourth years:
Appreciation for the third year = ($37,375 + $5,606.25) * 15% = $42,981.25 * 0.15 = $6,447.19
Appreciation for the fourth year = ($42,981.25 + $6,447.19) * 15% = $49,428.44 * 0.15 = $7,414.27
To calculate the current value of the painting, we add the initial value to the total appreciation over the four-year period:
Current value = $32,500 + $4,875 + $5,606.25 + $6,447.19 + $7,414.27 = $56,842.71
Rounding the result to the nearest $100, the painting is worth approximately $56,800 now.