How long will it take you to triple an amount of $500 if you invest it at a rate of 6% compounded annually?

Question

By using 

A=P(1+r/n)^nt

Answer 1

Hello, thank you for taking the time to post your question!

The formula that you want to use to solve this one is the compound interest formula

A = P(1 + r/n)^(nt)

A = final amount = 500 * 3 = 1500

P = principal = 500

r = interest rate = 6% = 0.06

n = compounds per year = 1

t = number of years = what we are solving for

that means that the underlying equation here for this scenario is

1500 = 500(1 + 0.06/1)^(1*t)

From there then you can solve for the value of “t” algebraically using logarithms! When I do that I end up getting t = 18.85, meaning that it will take about 19 years until the amount in the account triples.

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

A = P(1+r/n)^nt

 

We want to triple the initial investment P, so we want A = 3P

 

3P = P(1+r/n)^nt

 

3 = (1+r/n)nt           [Divided both sides by P]

 

For annual compounding, n=1.  Given r=0.06 (6% in decimal form):

 

3 = (1.06)^t

 

To solve for t, we need to get it out of the exponent; so take the log of both sides.  You can use any base log.  I'll use natural log (ln):

 

ln(3) = ln(1.06^t) = t*ln(1.06)                    [Identity: log(a^b) = b*log(a)]

 

ln(3)/ln(1.06) = t ≅ 18.85 years