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Chapter 6: Problem 8

You decide to invest 3000 dollars in a 1 -year certificate of deposit (CD) that earns an annual percentage yield (APY) of 2.4 \(\%\). How much will your investment be worth in a year?

Short Answer

Expert verified
Answer: The value of the investment after 1 year will be $3072.

Step by step solution

01

Understand the given information

We are given the following data: - Initial investment (Principal amount): $3000 - Annual percentage yield (APY): \(2.4\%\) - Investment duration: 1 year
02

Convert the interest rate to a decimal

To work with the interest rate in calculations, we need to convert it from a percentage to a decimal. Divide the percentage value by 100 to convert it to a decimal: Interest_rate_decimal = \(\frac{2.4}{100} = 0.024\)
03

Use the compound interest formula

Since we're working with annual compounding, we can use the following formula for compound interest: \(A = P(1 + r)^{t}\) Here, - A is the final amount after t years - P is the initial principal amount - r is the interest rate (as a decimal) - t is the number of years In our case, P = \(3000\), r = \(0.024\), and t = \(1\).
04

Calculate the final amount

Plug the values into the compound interest formula: \(A = 3000(1 + 0.024)^{1}\) To find the final value of the investment, perform the calculations: $A = 3000(1.024)^{1} \\ A = 3000 \times 1.024 \\ A = 3072$ So, the value of the investment after 1 year will be 3072 dollars.

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