Question

Regina recently inherited an oil painting that was purchased by her great-grandfather for $100 in 1938. In 2013 she took the painting to an appraiser who estimated its value at $300,000.
what was the annual percent of increase in the value of the painting?

Answer 1

The future worth of a certain item or money deposited at a certain percentage is obtained by the equation,

   F = P x (1 + i)^n

F is the future worth, P is present worth, i is the percentage, and n is the number of years.

   n = 2013 - 1938
   n = 75

Substituting the known values,

    300,000 = 100 x (1 + i)^75

The value of i from the equation is 0.1126.

The answer to this item is 11.26%. 

Answer 2

11.27% There are 2 things to calculate first. That being "over how many years?" and "by what factor?" So years first. 2013 - 1938 = 75 And now the factor 300000 / 100 = 3000 So the painting is worth 3000 times what it originally cost over a period of 75 years. And now all we need to do is calculate some number R such that R raised to the 75th power equals 3000. That is easily done with logarithms. We want the 75th root of 3000. So take the logarithm of 3000, divide by 75, and then take the anti-log. So R = 10^(log(3000)/75) - 1 R = 10^(3.477121255/75) - 1 R = 10^0.046361617 - 1 R = 1.1126578 - 1 R = 0.1126578 So the painting increased in value by 11.27% each year.