In 1626, peter minuit traded trinkets worth $24 for land on manhattan island. assume that in 2014 the same land was worth $6 trillion. find the annual rate of interest compounded continuously at which the $24 would have had to be invested during this time to yield the same amount. (round your answer to one decimal place.)

First compute how many years are there from 1626:
2014-1626= 388 years. 
Let the annual  rate be r. Then the formula is the following:

We solve the above equation in order to find the value of r like this:

Using a calculator we get:
r=0.05
The annual rate is then 5%

The principal is
P = $24
Calculate the duration.
t = 2014 - 1626 = 388 years
The value after 388 years is
A = $6 x 10⁹
For continuous compounding, the compounding interval is
n = 365

Let r =  the rate.
Then use the formula


That is,
Hence obtain
r/365 = 1.00013655 - 1 = 0.00013655
r = (0.00013655)*(365) = 0.0498 = 4.98%

5.0%  (to 1 decimal place)