SOLUTION: Kyle invests in an account earning 4.5% interest compounded continuously. How long will it take to double his investment? Doubling time in years =

Question 1198837: Kyle invests in an account earning 4.5% interest compounded continuously. How long will it take to double his investment?
Doubling time in years =
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
2 = e^(.045*t)
take natural log of both sides of the equation to get:
ln(2) = ln(e^(.045*t)
since ln(e^(.045*t) is equal to .045*t * ln(e) and since ln(e) = 1, the equation becomes:
ln(2) = .045*t
solve for t to get:
t = ln(2)/.045 = 15.40327068
that's how many years it will take for the money to double.
to confirm, replace t in the equation to get:
2 = e^(.045*15.40327068)
since e^(.045*15.40327068) = 2, the equation becomes:
2 = 2, confirming the value of t is correct.
your solution is it will take 15.40327068 years for the money to double.
note that e is the scientific constant of 2.718282828.....

RELATED QUESTIONS
Kyle Invests in an account earning 4.75% interest compounded continuously. How long will... (answered by MathLover1)

an account pays 5% interest, compounded continuously. how long will it take for the... (answered by jim_thompson5910)

An account pays 5% interest, compounded continuously. How long will it take for the... (answered by stanbon)

Thor invests some money in an account earning 8% interest, compounded continuously. After (answered by fractalier)

How long does it take for an initial investment of $2,500, earning 6.18% interest,... (answered by fractalier)

2. How long will it take $300 to grow to $450 in an account earning 5% interest... (answered by Boreal)

Gina puts $6500 into an account earning 7.75% interest compounded continuously. How long... (answered by htmentor)

If you invest a sum of money in an account earning 16% annual interest compounded... (answered by robertb)

suppose you deposit money in an investment account that pays 7% annual interest... (answered by scott8148)