document.write( "Question 761813: You just put $2193 in a CD that is expected to earn 17% compounded quarterly, and $7107 in a savings account that is expected to earn 3% compounded semiannually. Determine when, to the nearest year, the values of your two investments will be the same. \n" ); document.write( "
Algebra.Com's Answer #463558 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
You just put $2193 in a CD that is expected to earn 17% compounded quarterly, and $7107 in a savings account that is expected to earn 3% compounded semiannually. Determine when, to the nearest year, the values of your two investments will be the same.
\n" ); document.write( "***
\n" ); document.write( "Compound interest formula: A=P(1+r/k)^kn, P=initial investment, r=annual interest rate, k=number of compounding periods, n=number of years, A=amount after n-years
\n" ); document.write( "For CD:
\n" ); document.write( "P=$2193
\n" ); document.write( "r/k=.17/4=0.0425
\n" ); document.write( "kn=4n
\n" ); document.write( "..
\n" ); document.write( "Savings account:
\n" ); document.write( "P=$7107
\n" ); document.write( "i=.03/4=0.015
\n" ); document.write( "kn=2n
\n" ); document.write( "..
\n" ); document.write( "2193(1+.0425)^4n=7107(1+.015)^2n
\n" ); document.write( "2193(1.0425)^4n=7107(1.015)^2n
\n" ); document.write( "2193/7107=1.015^2n/1.0425^4n
\n" ); document.write( "Take log of both sides
\n" ); document.write( "log(2193/7107)=2nlog(1.015)-4nlog(1.0425)
\n" ); document.write( "-0.5106=2n(.006466)-4n(.018076
\n" ); document.write( "-0.5106=2n(.006466-2(.018076)
\n" ); document.write( "-0.5106=2n(0.02968)
\n" ); document.write( "2n=.5106/.02968≈17.2
\n" ); document.write( "n≈8.6≈9yrs
\n" ); document.write( "Values of the two investments will be the same after about 9 years \n" ); document.write( "
\n" );