SOLUTION: How long it will take for P 2500 to become P 3205.09 if it is invested at an interest rate of 5% compounded quartely?

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Question 1197286: How long it will take for P 2500 to become P 3205.09 if it is invested at an interest rate of 5%
compounded quartely?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
A=P%281%2Br%2Fn%29%5E%28nt%29

A = amount to become = 3205.09
P = principal = beginning amount = 2500
r = 5% = 0.05
n = 4 since compounding is quarterly, 4 times a year.

3205.09=2500%281%2B0.05%2F4%29%5E%284t%29

3205.09=2500%281%2B0.0125%29%5E%284t%29

3205.09=2500%281.0125%29%5E%284t%29

Divide both sides by 2500

1.282036=1.0125%5E%284t%29

Take natural logs of both sides

ln%281.282036%29=ln%281.0125%5E%284t%29%29

Move the exponent 4t in front of the natural log

ln%281.282036%29=4t%2Aln%281.0125%29

Solve for t by dividing both sides by 4*ln(1.0125)

ln%281.282036%29%2F%284%2Aln%281.0125%29%29=t

4.999980665=t

Round to t=5 years

Edwin