SOLUTION: Investing $8,000 for 6 years. Option #1 7% compounded monthly Option #2 6.85% compounded continuously Which is the better investment?

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Question 1208832: Investing $8,000 for 6 years.
Option #1
7% compounded monthly
Option #2
6.85% compounded continuously
Which is the better investment?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Option 1
A = P*(1+r/n)^(n*t)
A = 8000*(1+0.07/12)^(12*6)
A = 12160.84 approximately when rounding to the nearest penny

Option 2
A = P*e^(r*t) where e = 2.718 roughly
A = 8000*e^(0.0685*6)
A = 12066.60 approximately when rounding to the nearest penny

You earn slightly more with option 1.
The difference is 12160.84 - 12066.60 = 94.24 extra dollars.
Answer by ikleyn(52795)   (Show Source): You can put this solution on YOUR website!
.

In order for to determine which investment is better in this problem, 
there is no need to calculate the final future value after 6 years.


It is enough to count the effective growth factor in one year.


From one side hand, we have  the effective yearly growth factor of

     = 1.072290081...   (for 7% compounded monthly)


From the other side, we have the effective yearly growth factor 

     =  = 1.070900576...   (for 6.85% compounded continuously)


Where yearly effective yearly growth factor is greater, there the investment is better.


ANSWER.  Option 1 is better.

Solved.


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