Hello -- I have a question about the valuation (present value) of an annuity that makes payments more frequently than interest is compounded. The formulas presented in Broverman and Kellison will calculate this, but from my understanding of them it is necessary for interest to be paid/collected on fractional time periods (fractional of the compounding period). Is this true?

For example, if $100 is paid at the end of every month over the next year, and if we assume a interest of 4% compounded quarterly, the present value calculation on January 1, 2006 would have the first payment discounted by 100*(1.01)^(-1/3). But, doesn't this assume a fractional interest payment?

If fractional interest wasn't allowed, it seems to me that the present value would just be 300[(1.01)^(-1) + (1.01)^(-2) + (1.01)^(-3) + (1.01)^(-4)]. But, the two answers are not the same. What am I missing here?