Question

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

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

Step-by-step solution

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

Apply the formula for compound interest.

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

Substitute the given values into the formula.

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

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.