SOLUTION: An investment of $3000 earns 3.5% compounded semi- annually. a) what is the amount of the investment in 5 years? I got this A=3000(1+0.0175)^10 A=$3568.33 b) How long wil

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: An investment of $3000 earns 3.5% compounded semi- annually. a) what is the amount of the investment in 5 years? I got this A=3000(1+0.0175)^10 A=$3568.33 b) How long wil      Log On


   

Question 1167965: An investment of $3000 earns 3.5% compounded semi- annually.
a) what is the amount of the investment in 5 years?
I got this A=3000(1+0.0175)^10
A=$3568.33
b) How long will it take to double in value?
I am not sure how to do this one
Thanks


Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
You want to know how long it will take $3000 to grow to $6000.

A=P%281%2Br%2Fn%29%5E%28n%2At%29

6000=3000%281%2B0.035%2F2%29%5E%282t%29

Divide both sides by 3000

2=%281%2B0.0175%29%5E%282t%29

2=1.0175%5E%282t%29

Take logs of both side:

log%28%282%29%29=log%28%281.0175%5E%282t%29%29%29

Use the principle that states that the logarithm of an exponential
equals the product of the exponent with the logarithm of the base.

log%28%282%29%29=2t%2Alog%28%281.0175%29%29

Divide both sides by 2log(1.0175)





log%28%282%29%29%2F%282log%28%281.0175%29%29%29=t+

Use a scientific or graphing calculator to calculate the left side:

19.97699091=t

That rounds to 20 years.

Edwin