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)![]() ![]() You can put this solution on YOUR website! \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( " \n" ); document.write( "The variable is in an exponent; so to solve algebraically you need to use logarithms. \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "Use a calculator.... \n" ); document.write( "Or an easy path to the numerical answer is by graphing the two functions \n" ); document.write( " \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. \n" ); document.write( " \n" ); document.write( " |