document.write( "Question 193774: I have tried this equation numerous times.. but I can't seem to get the time. Here is the problem :\r
\n" ); document.write( "\n" ); document.write( "Find the time required for an investment of 5000 dollars to grow to 6400 dollars at an interest rate of 7.5 percent per year, compounded quarterly.\r
\n" ); document.write( "\n" ); document.write( "Here is what I have done: \r
\n" ); document.write( "\n" ); document.write( "6400=5000(1+(0.075/4))^4t
\n" ); document.write( "5000(1+(0.075/4))^4t=6400
\n" ); document.write( "5000(1+.01875)^4t=6400
\n" ); document.write( "5000/5000(1.01875)^4t=6400/5000
\n" ); document.write( "(1.01875)^4t=1.28
\n" ); document.write( "4t*ln(1.01875)=ln(1.28)
\n" ); document.write( "t=ln(1.28)/4*ln(1.01875) \n" ); document.write( "
Algebra.Com's Answer #145468 by Alan3354(69443)\"\" \"About 
You can put this solution on YOUR website!
I have tried this equation numerous times.. but I can't seem to get the time. Here is the problem :
\n" ); document.write( "Find the time required for an investment of 5000 dollars to grow to 6400 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
\n" ); document.write( "Here is what I have done:
\n" ); document.write( "6400=5000(1+(0.075/4))^4t
\n" ); document.write( "5000(1+(0.075/4))^4t=6400
\n" ); document.write( "5000(1+.01875)^4t=6400
\n" ); document.write( "5000/5000(1.01875)^4t=6400/5000
\n" ); document.write( "(1.01875)^4t=1.28
\n" ); document.write( "4t*ln(1.01875)=ln(1.28)
\n" ); document.write( "t=ln(1.28)/4*ln(1.01875)
\n" ); document.write( "--------------------
\n" ); document.write( "r = 1.01875 per quarter
\n" ); document.write( "5000*1.01875^p = 6400 (p = periods)
\n" ); document.write( "1.01875^p = 1.28
\n" ); document.write( "p*log(1.01875) = log(1.28)
\n" ); document.write( "p = log(1.28)/log(1.01875)
\n" ); document.write( "p = 13.288 quarters
\n" ); document.write( "p = ~ 3.32 years\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );