Question 201585
Compounded Quarterly:



{{{A=P(1+r/n)^(nt)}}} Start with the given equation.



{{{A=5000(1+0.045/4)^(4*5)}}} Plug in {{{P=5000}}}, {{{r=0.045}}}, {{{n=4}}}, and {{{t=5}}}



{{{A=5000(1+0.01125)^(4*5)}}} Divide



{{{A=5000(1+0.01125)^(20)}}} Multiply



{{{A=5000(1.01125)^(20)}}} Add



{{{A=5000(1.25075)}}} Raise 1.01125 to the 20th power to get 1.25075



{{{A=6253.75}}} Multiply



So the approximate return is $6,253.75




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Compounded Continuously:



{{{A=Pe^(rt)}}} Start with the given equation.



{{{A=5000e^(0.045*5)}}} Plug in {{{P=5000}}}, {{{r=0.045}}}, and {{{t=5}}}



{{{A=5000e^(0.225)}}} Multiply



{{{A=5000(1.25232)}}} Raise "e" (which is roughly 2.78...) to the 0.225 power to get 1.25232



{{{A=6261.6}}} Multiply



So the return is roughly $6,261.60



Since 6,253.75 < 6,261.60,  we can see that the compounded continuous investment  yields the better return.



Because 6,261.60 - 6,253.75 = 7.85, this means that the compounded continuous investment is better by about $8 (to the nearest dollar).



note: these values are approximations.