Question

Abc bank offers a savings account with 4.5% compounded quarterly. find the apy the bank's savings account offers (round your answer to three decimal places).

1) 2.5%
2) 3.5%
3) 4.5%
4) 5.5%

Answer 1

The correct option is 3). The APY for a savings account with a 4.5% nominal rate compounded quarterly is calculated using the formula APY = (1 + r/n)^(n*t) - 1. After plugging in the values and calculating, the APY is approximately 4.686%.

Step-by-step explanation:

The question revolves around finding the annual percentage yield (APY) that a bank offers on a savings account with 4.5% interest compounded quarterly. The APY formula that takes into account quarterly compounding is:

APY = (1 + r/n)^(n*t) - 1

where:

• r is the annual interest rate (as a decimal)
• n is the number of times interest is compounded per year
• t is the time in years

In this case, r is 4.5% or 0.045, n is 4 (since the interest is compounded quarterly), and t is 1 year. Plugging these values into the APY formula:

APY = (1 + 0.045/4)^(4*1) - 1

Calculating the above gives us the value:

APY = (1 + 0.01125)^4 - 1

APY = 1.046856 - 1

APY = 0.046856

Converted to percentage, APY = 4.6856%, which when rounded to three decimal places gives us 4.686%.

Therefore, the correct option is 3) 4.5%, as it's the closest to our calculated APY.