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Chapter 6: Problem 4

You deposit \(\$ 2000\) in a 5 -year certificate of deposit that pays \(4 \%\) interest compounded annully. To the nearest dollar, what balance will the account show when your certificate comes due?

Short Answer

Expert verified
Answer: Approximately $2434.

Step by step solution

01

Convert the given interest rate to decimal

To convert the interest rate from percentage to decimal, divide it by 100: \( Interest\; Rate\; (decimal) = \frac{4}{100} = 0.04 \)
02

Apply the compound interest formula

Now we will use the formula for compound interest: \( Future \; Value = Principal\, 脳\, (1\, +\, Interest\; Rate)^{Number\; of\; Compounding\; Periods} \) By substituting the values we have: \( Future\; Value = 2000\, 脳\, (1\, +\, 0.04)^5 \)
03

Calculate the future value

Compute the expression: \( Future\; Value = 2000\, 脳\, (1.04)^5 \) \( Future\; Value \approx 2433.601 \)
04

Round the final answer

To the nearest dollar, the balance when the certificate of deposit comes due is about: \( Future\; Value \approx \$2434 \)

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