SOLUTION: Hi in the formula A=P(1+i)^N the formula for compound interest how do you find what N equals with out having to guess and check. Thank you, Lachlan

Algebra ->  Equations -> SOLUTION: Hi in the formula A=P(1+i)^N the formula for compound interest how do you find what N equals with out having to guess and check. Thank you, Lachlan       Log On


   

Question 851560: Hi in the formula A=P(1+i)^N the formula for compound interest how do you find what N equals with out having to guess and check.
Thank you,
Lachlan
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Are you given +A+, +P+ and +i+ ?
Say they are given.
+A+=+2000+
+P+=+500+
+i+=+.06+
You are asked to find +N+
+A+=+P%2A%28+1+%2B+i+%29%5EN+
+2000+=+500%2A%28+1+%2B+.06+%29%5EN+
Divide both sides by +500+
+4+=+1.06%5EN+
Now you take the log of both sides
+log%284%29+=+log%28%28+1.06%5EN+%29%29+
+log%284%29+=+N%2Alog%28%28+1.06+%29%29+
+N+=+1og%284%29+%2F+log%28%28+1.06+%29%29+
+N+=+.6021+%2F+.0253+
+N+=+23.8+
So, it takes 24 yrs ( rounded off ) for $500
invested @ 6%, compounded annually to
become $2,000
check:
+2000+=+500%2A%28+1+%2B+.06+%29%5EN+
+2000+=+500%2A%28+1+%2B+.06+%29%5E24+
+4+=+1.06%5E23.8+
By my calculator:
+4+=+4.002+
close enough