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How long will it take for $5500 to grow to $22000 at 3% annual interest rate compounded quarterly?

 Apr 21, 2015

Best Answer 

 #2
avatar+129852 
+5

We have

22000 = 5000(1 + .03/4)^(4t)   divide both sides by 5000

22/5  = (1.0075)^(4t)   take the log of both sides

log(22/5)  = log(1.0075)^(4t)   and we can write

log(4.4) = (4t)*log(1.0075)   divide both sides by log(1.0075)

log(4.4)/log(1.0075)  = 4t     divide both sides by 4

log(4.4) / [4*log(1.0075)  = t ≈ 49.6 years

 

  

 Apr 22, 2015
 #1
avatar+66 
0

Just did this last week. You take the anual interest formula

A(t)=a(1+r)^t and insert ur variables. 5500(1+.03)^t

t equals time so do the guess and check method to figure it out.

actually no. subracy 5500 from 22000 and then figure it out. ur 

equation should look like this 16500(1+.03)^t and do guess and check.

If anybody knows any better methods write em down. im still a newbi at

this.

 Apr 21, 2015
 #2
avatar+129852 
+5
Best Answer

We have

22000 = 5000(1 + .03/4)^(4t)   divide both sides by 5000

22/5  = (1.0075)^(4t)   take the log of both sides

log(22/5)  = log(1.0075)^(4t)   and we can write

log(4.4) = (4t)*log(1.0075)   divide both sides by log(1.0075)

log(4.4)/log(1.0075)  = 4t     divide both sides by 4

log(4.4) / [4*log(1.0075)  = t ≈ 49.6 years

 

  

CPhill Apr 22, 2015

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