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Chapter 17: Problem 8

You open a 5-year CD for \(\$ 1,000\) that pays \(2 \%\) interest, compounded annually. What is the value of that \(\mathrm{CD}\) at the end of the five years?

Short Answer

Expert verified
At the end of the five years, the value of the CD is \(1104.08\).

Step by step solution

01

Write down the given values.

The given values are: - Initial principal balance (\(P\)): \(\$1,000\) - Interest rate (\(r\)): \(2\% = 0.02\) - Number of times compounded per year (\(n\)): 1 (annually) - Time duration (\(t\)): 5 years
02

Apply the formula for compound interest.

Now, we can apply the compound interest formula to calculate the final value of the CD: Final value \(= P(1 + \frac{r}{n})^{nt}\)
03

Substitute the given values into the formula.

Substitute the given values into the formula: Final value \(= 1000(1 + \frac{0.02}{1})^{1*5}\)
04

Calculate the final value.

Calculate the final value by following the order of operations (PEMDAS): Final value \(= 1000(1 + 0.02)^{5}\) Final value \(= 1000(1.02)^{5}\) Final value \(= 1000(1.1040808\) Final value \(= 1104.08\) The value of the CD at the end of the five years is $1104.08.

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