Answer:
To find the effective annual rate (EAR) of an account that pays interest at the nominal rate of 7% per year, compounded daily, we can use the following formula:
EAR = (1 + r/n)^n - 1
where r is the nominal annual interest rate (expressed as a decimal), and n is the number of times the interest is compounded in a year.
For daily compounding, n = 365 (since there are 365 days in a year), so we have:
EAR = (1 + 0.07/365)^365 - 1 = 0.0725 or 7.25%
To find the effective annual rate for hourly compounding, we need to adjust the value of n to account for the fact that interest is compounded more frequently. There are 365 days * 24 hours = 8,760 hours in a year, so we can use n = 8,760:
EAR = (1 + 0.07/8760)^8760 - 1 ≈ 0.0727 or 7.27%
Therefore, the effective annual rate for hourly compounding is approximately 7.27%.