According to a 2004 article by Doug Abrahms, the U.S. House of Representatives passed a bill to distribute funds to members of the Western Shoshone tribe.
The article says:
The Indian Claims Commission decided the Western Shoshone lost much of their land to gradual encroachment. The tribe was awarded $26 million in 1977. That has grown to about $145 million through compound interest, but the tribe never took the money.
Assuming monthly compounding the APR (that would give this growth in the award over the 27 years from 1977 to 2004) is ______%.
To calculate the annual percentage rate (APR) for monthly compounding growth, we will use the formula:
A = P(1 + r/n)^(n*t)
Where:
A = final amount
P = initial principal amount
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, we are given that the initial principal amount (P) is $26 million. The final amount (A) is $145 million. The time (t) is 27 years. Since we want to find the APR, we need to solve for the annual interest rate (r).
Let's substitute these values into the formula:
145,000,000 = 26,000,000(1 + r/12)^(12*27)
Now we need to solve for r. However, solving this equation directly would be quite tedious. Instead, we can use a numerical method like approximation or iteration to find the value.
One common method is the trial and error process, where we make an initial guess for r, plug it into the equation, see if it matches the right-hand side of the equation, and refine our guess until we get a close enough match.
Using this method, we can start with a reasonable guess, like 0.05 (or 5%). Plug it into the equation and check if it matches the right-hand side:
145,000,000 = 26,000,000(1 + 0.05/12)^(12*27)
If the left-hand side of the equation is greater than the right-hand side, our guess is too low. We increase the value of r and try again. If the left-hand side is smaller than the right-hand side, our guess is too high, so we decrease the value of r.
By repeating this process, we can narrow down our guess until we find a value of r that provides a close match between the left and right sides of the equation.