Final answer:
a) The APY is 7.13%. b) The amount at maturity is $9578.56. c) The APY and maturity value do not change with a different investment amount.
Step-by-step explanation:
a) To calculate the APY (Annual Percentage Yield), we can use the formula:
APY = (1 + r/n)^n - 1
where r is the annual interest rate and n is the number of compounding periods in a year.
For this CD, the annual interest rate is 7% and it is compounded quarterly (4 times a year). Plugging in the values, we have:
APY = (1 + 0.07/4)^4 - 1 = 0.07129 = 7.13%
Therefore, the APY is 7.13%.
b) To calculate the maturity value, we can use the formula:
Maturity Value = Principal * (1 + APY/n)^(n*t)
where Principal is the initial amount, APY is the annual percentage yield, n is the number of compounding periods in a year, and t is the number of years.
For this CD, the principal is $8000, the APY is 7.13%, n is 4 (compounded quarterly), and t is 30/12 = 2.5 years. Plugging in the values, we have:
Maturity Value = 8000 * (1 + 0.07129/4)^(4*2.5) = $9578.56
Therefore, the amount at maturity is $9578.56.
c) If the investment were $12000 for 18 months with the same APR and quarterly compounding, the APY and maturity value would not change because the APY and maturity value formulas do not depend on the initial investment amount.