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

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(35256) (Show Source): You can put this solution on YOUR website!
Compounded Quarterly:

Start with the given equation.

Plug in , , , and

Divide

Multiply

Add

Raise 1.01125 to the 20th power to get 1.25075

Multiply

So the approximate return is $6,253.75

-----------------------------------------------------

Compounded Continuously:

Start with the given equation.

Plug in , , and

Multiply

Raise "e" (which is roughly 2.78...) to the 0.225 power to get 1.25232

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.
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