SOLUTION: How do I solve for t? If A=$5000, P=$1000, r=2.5%, n=2, where A=P(1+r%/n)^(nt)? This is a compound interest problem using logarithm. Thank you

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: How do I solve for t? If A=$5000, P=$1000, r=2.5%, n=2, where A=P(1+r%/n)^(nt)? This is a compound interest problem using logarithm. Thank you      Log On


   

Question 840597: How do I solve for t? If A=$5000, P=$1000, r=2.5%, n=2, where A=P(1+r%/n)^(nt)? This is a compound interest problem using logarithm.
Thank you
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Find the logarithm of each side of the equation; do so symbolically first. Substitute the values later.

You will want the rate as a decimal fraction, but this solution is adjusted for keeping r as you gave it, as a decimal value as a percent quantity.
A=P%281%2Br%2F%28100n%29%29%5E%28nt%29.
ln%28A%29=ln%28P%29%2Bln%28%281%2Br%2F%28100n%29%29%5E%28nt%29%29
ln%28A%29-ln%28P%29=nt%2Aln%28%281%2Br%2F%28100n%29%29%29
highlight%28t=%28ln%28A%29-ln%28P%29%29%2F%28n%2Aln%281%2Br%2F%28100n%29%29%29%29
I chose natural logarithm, but you could just as well choose base ten or common logarithm.