Question

suppose that in 1605, a man bought a diamond worth the equivalent of $24. suppose that the man had instead been able to put the equivalent of $24 in a bank at 3% interest compounded continuously. what would that $24 have been worth in 2005?

in 2005, the $24 would have been worth $
(do not round until the final answer. then round to the nearest dollar as needed.)

Explanation:

Step1: Calculate the time period

The time period \(t\) from 1605 to 2005 is \(2005 - 1605=400\) years.

Step2: Use the continuous - compounding formula

The formula for continuous compounding is \(A = Pe^{rt}\), where \(P=\$24\), \(r = 0.05\) (since \(5\%=0.05\)), and \(t = 400\).
Substitute the values into the formula: \(A=24e^{0.05\times400}\).
First, calculate \(0.05\times400 = 20\). Then \(A = 24e^{20}\).
We know that \(e^{20}\approx485165195.4\).
So \(A=24\times485165195.4\).

Answer:

\(11643964690\)