# word problem using logarithms

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• Dec 2nd 2009, 02:48 AM
extraordinarymachine
word problem using logarithms
can someone plese help me with this question, how to set it up and solve it. thanks!

a savings bond offers intrest at a rate of 6.6%, compounded semi-annually. suppose that a \$500 bond is purchased. how long will it take for the investment to double in value.?
• Dec 2nd 2009, 05:27 AM
LochWulf
If you're familiar with the basic 'single investment, compounding forward' set-up...

$500\left(1 \ + \ \frac{0.066}{2}\right)^n \ = \ F$

...where F is the amount the initial investment will grow to after n periods, the solution to your question starts with that basic layout:

$500\left(1 \ + \ \frac{0.066}{2}\right)^n \ = \ 1,000$

which immediately reduces to

$\left(1 \ + \ \frac{0.066}{2}\right)^n \ = \ 2$

Now solve for n. Start by taking the logs of both sides, and remember that $\text{ln}(a^b) \ = \ b\cdot \text{ln}(a)$. Finally, remember that in this set-up, n represents the number of semi-annual periods it'll take for the investment to double...so you might wanna re-express it as years in your final answer.
• Dec 2nd 2009, 06:16 PM
TKHunny
Please do not forget the remarkably reliable "Rule of 72s". For reasonable interest rates, the precision is almost always more than expected.

Since 6.6% is used semi-annually, we'll use 3.3% and calculate semi-annual periods.

72 / 3.3 = 21.818, just a little too high.