Question

Suppose a savings and loan pays a nominal rate of 4.6​% on savings deposits. Find the effective annual yield if interest is compounded daily. Assume that the year is not a leap year.

Answer 1

Nominal annual rate = 4.6%, is the rate when compounding is meant to be done only one time in a year.

No of days in a year = 365

Daily nominal rate = 4.6% / 365 = 0.046 / 365 = 0.000126

1 + Effective annual yield = (1 + Daily nominal rate)³⁶⁵

Effective annual yield = (1 + Daily nominal rate)³⁶⁵ -1

= (1+0.000126)³⁶⁵ - 1

= 1.047071 -1

= 0.047071

= 4.7071%

Or we can use the direct formula as,

where r = Nominal rate

m = No of times the interest is compounded

So we can use the above formula if the interest is compounded daily, monthly, quarterly and semi annually. Only m value changes in each case.

In our question, m = 365. So if we substitute r = 4.6% and m = 365, we get Effective annual yield as 4.7071%