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The amount of money in an account with continuously compounded interest is given by the formula A = Pert, where P is the principal, r is the annual interest rate, and t is the time in years. Calculate to the hundredth of a year how long it takes for an amount of money to double if interest is compounded continuously at 6.5%.

please help!

the formula is A=Pe^rt, I assume yours was a typo

Consider any Principal, eg P=100
so you want
200 = 100e^(.065t)
2 = e^.065t
.065t=ln 2

I got t=10.66 using my calculator

so you can use anything you want for the principal?

yes
we could have simply used the principal P
Since we want it to "double" the amount would then be 2P

2P = P e^(.065t), divide by P and we get

2 = e^.065t like before

oh okay, thanks!

The amount of money in an account with continuously compounded interest is given by the formula A=Pe^rt , where P is the principal, r is the annual interest rate, and t is the time in years. Calculate to the nearest hundredth of a year how long it takes for an amount of money to double if interest is compounded continuously at 6.2%. Round to the nearest tenth.

You're welcome! I'm glad I could help. Do you have any more questions?

You're welcome! I'm glad I could help. Remember, in this case, we used the formula A = Pe^rt for continuously compounded interest, where A is the amount in the account, P is the principal, r is the annual interest rate, and t is the time in years. We set up the equation 2 = e^(0.065t) to find when the amount doubles. We then solve for t by taking the natural logarithm of both sides to get 0.065t = ln(2) and dividing by 0.065. This gives us t ≈ 10.66 years. Let me know if there's anything else I can assist you with!