According to legend, manhattan islansd was purchased in 1626 for 24 dollars. If the 24 dollars have been invested instead at a rate of 6% interest per year, what would its value be in 2011?
v = 24 (1 + .06)^385
To calculate the value of $24 invested at an interest rate of 6% per year from 1626 to 2011, we need to use the compound interest formula. The formula is as follows:
A = P * (1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times that interest is compounded per year
t = number of years
In this case, the principal amount (P) is $24, the annual interest rate (r) is 6% (or 0.06 as a decimal), the number of times compounded per year (n) is usually not specified in historical data, so we will assume it's compounded annually. Lastly, the number of years (t) is 2011 - 1626 = 385.
Plugging these values into the formula:
A = 24 * (1 + 0.06/1)^(1*385)
A = 24 * (1.06)^385
Now we can calculate the value of $24 in 2011:
A ≈ 24 * 5,964.80
A ≈ $143,155.20
Therefore, if $24 was invested at a 6% interest rate per year from 1626 to 2011, its value would be approximately $143,155.20 in 2011.