suppose that in 1637, a man bought a diamond with the equivalent of $35. suppose that the man had instead…

suppose that in 1637, a man bought a diamond with the equivalent of $35. suppose that the man had instead been able to put the equivalent of $35 in a bank at 3% interest compounded continuously. what would that $35 have been worth in 2004?\nin 2004, the $35 would have been worth $ \n(do not round until the final answer. then round to the nearest dollar as needed.)

suppose that in 1637, a man bought a diamond with the equivalent of $35. suppose that the man had instead been able to put the equivalent of $35 in a bank at 3% interest compounded continuously. what would that $35 have been worth in 2004?\nin 2004, the $35 would have been worth $ \n(do not round until the final answer. then round to the nearest dollar as needed.)

Answer

Explanation:

Step1: Identify the compound - interest formula

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years.

Step2: Determine the values of $P$, $r$, and $t$

$P=$35$, $r = 0.03$ (since $3%=0.03$), and $t=2004 - 1637=367$ years.

Step3: Substitute the values into the formula

$A = 35\times e^{0.03\times367}$. First, calculate the exponent: $0.03\times367 = 11.01$. Then, find $e^{11.01}$. Using a calculator, $e^{11.01}\approx6634.23$. Multiply by the principal: $A = 35\times6634.23=232198.05$.

Answer:

$232198$