Continuously compunded interest

[Quantum_Grid]

Homework Statement

The island of Manhattan was sold for $24 in 1626. Suppose the money had been invested in an account which compounded interest continually.

a) How much money would be in the account in the year 2005 if the yearly interest rate was:
i: 5%? ii: 7%

The Attempt at a Solution

I put the numbers into the function P₀e^rt and got

i:24e^.05(379) and ii:24e^.07(379)

but when I put that in my calculator I get VERY large numbers:

i: 4074662794 and ii: 7.980752573_E12

For some reason, I don't think the homework answers would be such ridiculously large numbers. Did I do this right?

 

[Dick]

The numbers are ridiculously large but that doesn't mean they are wrong. Exponential growth is fast and 379 years is a ridiculously long time. I think you are correct.