Question

suppose $5,000 is invested in an account at an annual interest rate of 2.7% compounded continuously. how long (to the nearest tenth of a year) will it take the investment to double in size?

Answer 1

The basic equation for continuous compounding is as follows:

`A=Pe^(rt)`
Plugging in the given values gives:

`10000=5000e^(0.027t)`
Dividing both sides by 5000, we get:

`2=e^(0.027t)`
Take natural logs of each side:

`ln\ 2=0.027t`
from which we find that t = 25.67 years.