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Chapter 8: Problem 15

Suppose that you have \(\$ 12,000\) to invest. Which investment yields the greater return over three years: \(7 \%\) compounded monthly or \(6.85 \%\) compounded continuously?

Short Answer

Expert verified
To find the answer, calculate the investment returns using the above steps and compare. The investment that yields the larger return is the better option.

Step by step solution

01

Calculate Return for 7% Compounded Monthly

First, you need to calculate the return for the first investment option: 7% compounded monthly. Use the formula \(A = P(1 + r/n)^{nt}\). Here, \(P = \$ 12000\), \(r = 7/100 = 0.07\), \(n = 12\) (as it is compounded monthly), and \(t = 3\) years. Plug these values in to get \(A = \$ 12000 \times (1 + 0.07 / 12) ^ {12 \times 3}\)
02

Calculate Return for 6.85% Compounded Continuously

Next, calculate the return for the second investment option: 6.85% compounded continuously. Use the formula \(A = P e^{rt}\). Here, \(P= \$ 12000\), \(r = 6.85/100 = 0.0685\), and \(t = 3\) years. Plug these values in to get \(A = \$ 12000 \times e^{0.0685 \times 3}\)
03

Compare the Two Returns

Finally, compare the two return values to identify which investment yields a greater return. If the first value is larger, then 7% compounded monthly yields a higher return. If the second, then 6.85% compounded continuously yields a higher return.

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