SOLUTION: Use the compound interest models A=P(1+r/n)^nt and A=Pe^rt to answer this question. Suppose you want to invest $5000. What investment yields the greater return over 5 years: 4.5% c

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Question 201585: Use the compound interest models A=P(1+r/n)^nt and A=Pe^rt to answer this question. Suppose you want to invest $5000. What investment yields the greater return over 5 years: 4.5% compound quarterly or 4% compound continuously? How much more, to the nearest dollar, is yielded by the better investment? PLEASE HELP.
Answer by jim_thompson5910(28595) About Me  (Show Source):
You can put this solution on YOUR website!
Compounded Quarterly:


A=P%281%2Br%2Fn%29%5E%28nt%29 Start with the given equation.


A=5000%281%2B0.045%2F4%29%5E%284%2A5%29 Plug in P=5000, r=0.045, n=4, and t=5


A=5000%281%2B0.01125%29%5E%284%2A5%29 Divide


A=5000%281%2B0.01125%29%5E%2820%29 Multiply


A=5000%281.01125%29%5E%2820%29 Add


A=5000%281.25075%29 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%5E%28rt%29 Start with the given equation.


A=5000e%5E%280.045%2A5%29 Plug in P=5000, r=0.045, and t=5


A=5000e%5E%280.225%29 Multiply


A=5000%281.25232%29 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.