SOLUTION: hi, I am having trouble understanding this question: Five years ago Greg invested $1500 at a fixed interest rate compounded quarterly. His investment is currently valued at $28

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Question 954819: hi,
I am having trouble understanding this question:
Five years ago Greg invested $1500 at a fixed interest rate compounded quarterly. His investment is currently valued at $2800. Using logs determine the annual rate of interest?
I do not understand how to find the interest rate without knowing how many years it took to grow.
thanks

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
His investment started +5+ years ago
Use the formula:
+A+=+P%2A%28+1+%2B+r%2Fn+%29%5E%28n%2At%29++
+P+=+1500+
+A+=+2800+
+t+=+5+
+n+=+4+
------------------
+2800+=+1500%2A%28+1+%2B+r%2F4+%29%5E%28+4%2A5%29+
+%28+1+%2B+r%2F4+%29%5E20+=+2800%2F1500+
+%28+1+%2B+r%2F4+%29%5E20+=+1.8667+
Take the log of both sides
+log%28%28+%28+1+%2B+r%2F4+%29%5E20+%29%29+=+log%28+1.8667+%29+
+20%2Alog%28%28+1+%2B+r%2F4+%29%29+=+log%28+1.8667+%29+
+log%28%28+1+%2B+r%2F4+%29%29+=+%281%2F20%29%2A.27107+
+log%28%28+1+%2B+r%2F4+%29%29+=+.0135535+
+1+%2B+r%2F4+=+10%5E.0135535+
+1+%2B+r%2F4+=+1.0317+
+r%2F4+=+.0317+
+r+=+.1268+
The annual rate is 12.68%
-------------------------
check:
------------------
+2800+=+1500%2A%28+1+%2B+r%2F4+%29%5E20+
+2800+=+1500%2A%28+1+%2B+.1268%2F4+%29%5E20+
+2800+=+1500%2A%28+1+%2B+.0317+%29%5E20+
+2800+=+1500%2A%28+1.0317+%29%5E20+
+2800+=+1500%2A1.86667+
+2800+=+2800.0119+
close enough