SOLUTION: Suppose that you have $3000 to invest. Which investment yields the greater return over 10 years: 8.75% compounded continuously or 8.9% compounded semiannually?

Question 960012: Suppose that you have $3000 to invest. Which investment yields the greater return over 10 years: 8.75% compounded continuously or 8.9% compounded semiannually?
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Suppose that you have $3000 to invest. Which investment yields the greater return over 10 years: 8.75% compounded continuously or 8.9% compounded semiannually?
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Continuous at 8.75%::
A(10) = 3000*e^(0.0875*10) = $7196.63
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8.9% compounded semiannually::
A(10) = 3000(1+(0.089/2)]^(2*10) = $7166.22
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Cheers,
Stan H.
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Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
8.75% compounded continuously

Note: 'e' is the constant 2.718 approximately (it's a lot like pi)

Use a calculator for this step

Use a calculator for this step

If you invest $3000 over 10 years at 8.75% interest compounded continuously, you'll have $7,196.63 in the account. Circle this value since you'll come back to it.

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8.9% compounded semiannually

For the second compounded annually option, we'll have $7,166.22 in the account

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Summary:

8.75% compounded continuously will have $7,196.63 in the account after the 10 yr period
8.9% compounded semiannually will have $7,166.22 in the account after the 10 yr period

So the first option "8.75% compounded continuously" is the better option since you're earning roughly $30 more.
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