document.write( "Question 1174220: An investment of $4950 earns 11%/a compounded semi-annually. How long will it take for the investment to grow to $9411? \n" ); document.write( "
Algebra.Com's Answer #799607 by greenestamps(13198)\"\" \"About 
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\n" ); document.write( "annual interest rate: 11% = 0.11
\n" ); document.write( "periodic interest rate (twice a year): 5.5% = 0.055
\n" ); document.write( "periodic growth factor: 1+0.055 = 1.055

\n" ); document.write( "The value after n compounding periods is the initial investment, multiplied by the periodic growth factor n times.

\n" ); document.write( "You want to know how long it will take the original $4950 to grow to $9411:

\n" ); document.write( "\"9411+=+4950%281.055%5En%29\"

\n" ); document.write( "The variable is in an exponent; so to solve algebraically you need to use logarithms.

\n" ); document.write( "\"1.055%5En+=+9411%2F4950\"
\n" ); document.write( "\"n%2Alog%28%281.055%29%29+=+log%28%289411%2F4950%29%29\"
\n" ); document.write( "\"n+=+log%28%289411%2F4950%29%29%2Flog%28%281.055%29%29\"

\n" ); document.write( "Use a calculator....

\n" ); document.write( "Or an easy path to the numerical answer is by graphing the two functions \"9411\" and \"4950%281.055%5En%29\" on a graphing calculator and find that they intersect at n=12.

\n" ); document.write( "\"graph%28600%2C400%2C-2%2C16%2C-2000%2C12000%2C4950%281.055%5Ex%29%2C9411%29\"

\n" ); document.write( "Then remember that n=12 is the number of compounding periods; since the compounding is twice a year, the length of time required for the investment to grow to $9411 is 12/2 = 6 years.

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