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Chapter 10: Problem 6

Paul invested the stock profits he received 15 years ago in an account that paid \(8 \%\) interest compounded quarterly. If his account now has \(\$ 7218.27\) in it, what was his initial investment?

Short Answer

Expert verified
Paul's initial investment was calculated using the compound interest formula rearranged to solve for the principal amount. Finally, by replacing known values and calculating the expression, we have found the initial investment made by Paul.

Step by step solution

01

Rearrange the compound interest formula

We start with the compound interest formula \(A = P(1 + r/n)^{nt}\) and rearrange it to solve for \(P\): \(P = A / (1 + r/n)^{nt}\)
02

Substitute the known values into the rearranged formula

Now we substitute the values into the rearranged formula: \(P = 7218.27 / (1 + 0.08/4)^{4 * 15}\)
03

Calculate the value of \(P\)

By calculating the above expression, we get the value of \(P\). \(P\) is the initial investment of Paul. Remember to round to the nearest cent if necessary.

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