Bank One offered a 20-year certificate of deposit (CD) at $4.5 \%$ interest compounded quarterly. On the same day on the Internet, First Bank offered a 20 -year CD at $4.49 \%$ compounded monthly. Find the APY for each CD. Which bank paid a higher APY? The APY for the CD at Bank One is $\square \%$. (Type an integer or decimal rounded to three decimal places as needed.) The APY for the CD at First Bank is $\square \%$. (Type an integer or decimal rounded to three decimal places as needed.) Which bank paid a higher APY? A. Bank One B. First Bank Next Search
Solution
Step 1 ：Given that Bank One offers a 20-year certificate of deposit (CD) at $4.5 \%$ interest compounded quarterly and First Bank offers a 20 -year CD at $4.49 \%$ compounded monthly, we are to find the APY for each CD and determine which bank paid a higher APY.
Step 2 ：The APY (Annual Percentage Yield) is a measure of how much money you would earn/owe in a year if you were to put money in that account. The formula for APY is: \(APY = (1 + r/n)^{nt} - 1\) where: r is the annual interest rate (decimal), n is the number of compounding periods per year and t is the time the money is invested for in years.
Step 3 ：For Bank One, r = 4.5/100 = 0.045, n = 4 (quarterly compounding), and t = 20 years. For First Bank, r = 4.49/100 = 0.0449, n = 12 (monthly compounding), and t = 20 years.
Step 4 ：We can calculate the APY for each bank using these values and then compare them to find out which bank paid a higher APY.
Step 5 ：For Bank One, \(APY = (1 + 0.045/4)^{4*20} - 1 = 1.4472749769708035\).
Step 6 ：For First Bank, \(APY = (1 + 0.0449/12)^{12*20} - 1 = 1.4505786261950426\).
Step 7 ：The APY for Bank One is approximately 1.447 or 144.7% and the APY for First Bank is approximately 1.450 or 145.0%.
Step 8 ：Therefore, First Bank paid a higher APY.
Step 9 ：Final Answer: The APY for the CD at Bank One is \(\boxed{144.7 \%}\). The APY for the CD at First Bank is \(\boxed{145.0 \%}\). The bank that paid a higher APY is \(\boxed{\text{First Bank}}\).
