Econ 350:  Computing YTM on zero bonds. The following formula should work every time:

YTM (yield compounded weekly)= (P1/P0)^(52/n) - 1.

Example: P1=1000: maturity value: also known as face value

P0: Purchase price= 800, n= time period in weeks . For a 10 year bond n= 10*52. Let us compute the YTM.

YTM= (1000/800)^(52/520)-1 = 0.022 or 2.2 %.

For yearly compounding, the exponent will be 1/n; for daily compounding the exponent is 365/n.

This formula is based on the familiar FV formula that you are familiar with:

P1= P0(1+i)^n.  By dividing both sides by P0, we have:

P1/P0 = (1+i)^n.  Taking the nth root of both sides we have:

(P1/P0)^(1/n) = 1+i.  Where is can be interpreted as the YTM.  Rearranging the terms, we have:

YTM=i= (P1/P0)^(1/n).