PreCalc question?

Question

In 1626, Peter Minuit traded trinkets worth $24 for land on Manhattan Island. Assume that in 2014 the same land was worth $7 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.

Answer 1

P*exp(r*t) = I

 

where P is the starting principal, r is the interest rate, t is the time, I is the interest earned.

 

24 * exp(r*(2014 - 1626) = 7 trillion

 

24 * exp( r * 388) = 7 trillion

 

exp(r * 368)  = 7 trillion / 24 = 291 666 666 666 and 2/3

 

r * 368 = ln ( 291 666 666 666 and 2/3)

 

r = ln ( 291 666 666 666 and 2/3)/368

 

r = 0.07174

or almost 7.2%

Answer 2

7,000,000,000 = 24e^r(388)

291,666,666.67 = e^388r

ln 291,666,666.67 = 388r

 

You can complete