# SOLUTION: How many years does it take for an investment to double in value if it is invested at 6% if interest is compounded quarterly? if interest is compounded continuously? thanks

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 Question 598014: How many years does it take for an investment to double in value if it is invested at 6% if interest is compounded quarterly? if interest is compounded continuously? thanksAnswer by lwsshak3(6761)   (Show Source): You can put this solution on YOUR website!How many years does it take for an investment to double in value if it is invested at 6% if interest is compounded quarterly? if interest is compounded continuously? ** compound interest formula: A=P(1+r)^t, P=initial investment, r=interest rate per period, t=number of periods, A=amount after t periods. For continuous compounding: A=Pe^rt .. Quarterly compounding: A/P=2, r=.06/4=.015, t=quarters A=P(1+r)^t A/P=(1+.06/4)^t A/P=(1+.015)^t 2=(1.015)^t take log of both sides log(2)=t*log(1.015) t=log(2)/log(1.015) t≈46.55 qtrs≈11.64 years .. Continuous compounding: A/P=2, r=.06, t=years A=Pe^rt A/P=e^rt 2=e^rt 2=e^.06t take log of both sides ln2=.06t*lne lne=1 .06t=ln2 t=ln2/.06 t≈11.55 years