SOLUTION: About how many years will it take for $1,800 to reach $2,500 at a simple interest rate of 4%

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Question 538590: About how many years will it take for $1,800 to reach $2,500 at a simple interest rate of 4%
Answer by jpg7n16(66) About Me  (Show Source):
You can put this solution on YOUR website!
For this problem, we are dealing with the compounding of an investment. The formula for compounding an investment is:
p%2A%28%281%2Bi%29%5En%29=x
'P' is initial principal; 'i' is interest rate in the compounding period; 'n' is the number of compounding periods; and 'x' is the final amount of the investment. So we should start looking for the pieces of the puzzle that we know. From the question:
p=1800;x=2500; and i=.04
The only piece we don't know is "n" - so that's what we'll be solving for. Plug what we do know into the equation.
1800%2A%28%281%2B.04%29%5En%29=2500
Now we start taking things away to leave "n" by itself. Start with 1800.
%281800%2A%281.04%5En%29%29%2F1800=2500%2F1800
Which leaves us with
1.04%5En=2500%2F1800
The tricky part is, how do you get that exponent down?? The answer: take the natural log of both sides. (Since ln%28a%5Ex%29=x%2Aln%28a%29)
ln%281.04%5En%29=ln%282500%2F1800%29
n%2A%28ln%281.04%29%29=ln%282500%2F1800%29
Now you have something you can work with. Just divide by anything that's not 'n'
%28n%2A%28ln%281.04%29%29%29%2Fln%281.04%29=ln%282500%2F1800%29%2Fln%281.04%29
n=ln%282500%2F1800%29%2Fln%281.04%29=8.375
You will reach $2,500 in approx. 8.375 years.