(Last Updated On: January 9, 2020)
Problem Statement: CE Board May 1995
How long (in years) will it take money to quadruple if it earns 7% compounded semi-annually?
- A. 20.15
- B. 26.30
- C. 33.15
- D. 40.30
Problem Answer:
The money will be quadruple in 20.15 years if it earns 7% compounded semi-annually.
Solution:
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Larry M.
Algebra
1 year, 2 months ago
We don’t have your requested question, but here is a suggested video that might help.
Related Question
How long will it take money to quadruple if it is invested at 8% compounded quarterly? 5.3% compounded continuously? It will take about nothing years at 8% compounded quarterly. (Round to two decimal places as needed.)
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Video Transcript
Okay for the compounding quarterly problem. Your formula is B for balance equals P principle Times one plus the interest rate divided by in to the end Times T. Power. Let P equal $1 and let B equal $4. In other words quadruple. Your principal says, how long will it take to quadruple? So you can pick any dollar amount for P. And then you quadruple it to make it be so why not choose one and four? RS .08. The interest rate and is four for compounding quarterly. So if I make all those substitution four equals one times one plus point oh eight divided by four to the 14. Now all of this stuff In the parentheses is just 1.02. So the equation becomes four equals 1.02 to the 14th. Now change that to its lab arrhythmic form. You have log base 1.02 of four equals 14. And now divide both sides by four And you have log base 1.02 of four Divided by four equals team. Enter that into your calculator and you'll see it's going to take 17.5 years compounded quarterly. Now for compounding continuously. The formula is different. B for balance equals P. For principal times E. The natural number two. The R. T. Power. So once again why not just let PB one and quadruple it and let be the balance before. So you have four equals one times E. To the point oh eight E. R. Is still um 8%. Okay. Now What you have is the natural log of four equals .080. My apologies. I'm just realizing that this .08 is not correct. That is supposed to be .053 T. So let's replace that exponent with .053 T. Okay. And so now you would have law natural log of four equals .053 T. And now you do it the same way except now you're going to be dividing by .053. So let's see .053. So if I grab my calculator, what is the natural log of Poland? Mm hmm, mm hmm. .3 is 26.2 years. So this answer is actually 26, Few years instead of 17.3 years.