Question

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!

Answer 1

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.