# word problem using logarithms

• Dec 2nd 2009, 01:48 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 $500 bond is purchased. how long will it take for the investment to double in value.? • Dec 2nd 2009, 04:27 AM LochWulf If you're familiar with the basic 'single investment, compounding forward' set-up...$\displaystyle 500\left(1 \ + \ \frac{0.066}{2}\right)^n \ = \ F $...where F is the amount the initial investment will grow to after n periods, the solution to your question starts with that basic layout:$\displaystyle 500\left(1 \ + \ \frac{0.066}{2}\right)^n \ = \ 1,000 $which immediately reduces to$\displaystyle \left(1 \ + \ \frac{0.066}{2}\right)^n \ = \ 2 $Now solve for n. Start by taking the logs of both sides, and remember that$\displaystyle \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, 05:16 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.