The annual interest rate r, when compounded more than once a year, results in a slightly higher yearly interest rate; this is called the annual (or effective) yield and denoted as Y. For example, $1000 deposited at 5%, compounded monthly for 1 yr (12 months), will have a value of A = 1000 ( 1 + 0.05 12 ) 12 = $ 1051.16 . The interest earned is $51.16/$1000, or 0.05116, which is 5.116% of the original deposit. Thus, we say this account has a yield of Y = 0.05116 , or 5.116%. The formula for annual yield depends on the annual interest rate r and the compounding frequency n:

Y = ( 1 + r n ) n − 1 .

For Exercises 41-48, find the annual yield as a percentage, to two decimal places, given the annual interest rate and the compounding frequency.

Annual interest rate of 5.3%, compounded monthly