how long does it take for a deposit of $1300 to double at 3% compounded continuously

Answer 1

Greetings! Lets solve this shall we ?

Let the compound continuously formula yield

A = Pe^rt

Then we must find out how long will it take for the initial investment to double at the rate of 3%? So, we take the initial investment of 1300 and double it making 2600 and plugging in the rate of interest such that

2600 = 1300e^(0.03)(t)..................We must solve this equation for the time t in years. First we divide 1300 to both sides such that

2 = e^(0.03)(t).................. Then we natural log both sides such that

ln(2) = lne^(0.03)(t)................Then bring the 0.03t down in front to get

ln(2) = (0.03t)lne.............lne equals 1 then we divide 0.03 to both sides to obtain

(ln2/0.03) = t .............Put this into the calculator to approximate the number of years it will take for the investment to double. Finally,

t = (ln2/0.03) = 23.1 years (or months depending on what the answer should be expressed in)

I hope this helped!