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Find the annual percentage yield (APY) in the following situation.

A bank offers an APR of 4.5% compounded daily.

User Amaralbf
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1 Answer

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Final answer:

The Annual Percentage Yield (APY) for an account with a 4.5% annual percentage rate (APR), compounded daily, can be calculated using the APY formula, resulting in an APY of approximately 4.56%.

Step-by-step explanation:

To calculate the annual percentage yield (APY) for an account with an annual percentage rate (APR) of 4.5%, compounded daily, we use the formula for APY, which includes the effect of compounding:

APY = (1 + r/n)^(n∗t) - 1

where:

r is the annual interest rate (decimal),

n is the number of times the interest is compounded per year,

and t is the time in years.

For daily compounding, n would be 365. As we're looking for the yield over one year, t will be 1. Converting the APR from a percentage to a decimal, we get r = 0.045. Substituting into the formula, we get:

APY = (1 + 0.045/365)^(365∗t) - 1

APY = (1 + 0.00012328767123)^(365) - 1

APY = 1.0456436200818 - 1

APY = 0.0456436200818

Converting this back into a percentage, we multiply by 100:

APY = 4.56436200818%

Thus, the Annual Percentage Yield for an account with a 4.5% APR compounded daily is approximately 4.56%.

User TheGambler
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