# Calculating the Cost of Delay

I am working on a problem in Davidson and Herskovitz workbook titled the Mortgage-Backed Securities Workbook. The questions asks to find the total opportunity cost to the investor of having a \$1 million cashflow delayed for 15 days and the current risk free interest rate is 6.5% actual/actual. I first converted 6.5% into a daily rate and then tried to compound the interest on 1 million dollars, but it was deemed incorrect. The correct answer is 2671.23.

Their is also an example, but this time the current risk free rate is 6.25% and the book tells us each delay costs 171.23. The investor is still supposed to receive 1 million. I am assuming one could take the 171 multiply it by 15 to get the total, but why not 14 to account for timing?

• By convention, for periods less than 6 months here is no compounding, it is just linear ("simple interest"): (15/365)*0.065 = 0.0267123 Apr 3, 2017 at 13:49
• I would put that as an answer Apr 3, 2017 at 14:26

## 1 Answer

These calculations are a matter of convention and standard practice (which are somewhat arbitrary, and not necessarily the way I would have defined it).

A compounding period is defined, which is by default 1 year (except for US treasuries where it is 6 months). For periods shorter than this, compounding is not used, but rather "simple interest" is used, which amounts to a linear interpolation. So for "15 days and the current risk free interest rate is 6.5% actual/actual" we would do (15/365)*0.065 = 0.0267123 . On 1 million it is 2671.23