Question

1. Kellie has $6,000 to invest. A local bank offers a 30-month CD with an APR of 3.8% compounded monthly. What is the APY? (Round your answer to three decimal places.)

2. Mariah has $9,000 to invest. A local bank offers a 24-month CD with an APR of 3.8% compounded monthly. What is the APY? (Round your answer to three decimal places.)
3. Compare the APY results. Which of the following statements is true?
a. Kellie's CD has a higher APY because her money is invested for a longer period of time than Mariah's.
b. Mariah's CD has a higher APY because the amount of money she is investing is greater than Kellie's.
c. Their CDs have the same APY because they have the same number of compoundings per year and the same APR. The amount invested and the time period of the investment don't matter because they aren't part of the APY formula.

Answer 1

Kellie and Mariah's CDs will have the same APY of approximately 3.876% because APY is calculated using the APR and the number of compounding periods per year, both of which are the same for both CDs.

Step-by-step explanation:

To find the Annual Percentage Yield (APY), we use the formula APY = (1 + r/n)n - 1, where r is the annual interest rate and n is the number of times the interest is compounded per year. In both cases, the APY can be calculated using the given APR of 3.8% (or 0.038) compounded monthly (n = 12).

For both Kellie and Mariah, we calculate APY as follows: APY = (1 + 0.038/12)12 - 1. After calculation, we find that the APY is approximately 0.038760, or 3.876% when rounded to three decimal places.

Therefore, the answer to statement 3 is c. Their CDs have the same APY because they have the same number of compoundings per year and the same APR. The amount invested and the time period of the investment don't affect the APY calculation.