How do you calculate bond equivalent yield of a bond knowing only the purchase price and face value?

I get 4.82% in the following way.

As 50000/49414.72 = 1.01184 the 3 month gain is 1.184%

To get the yield in a year take the fourth power

1..01184^4=1.0482 of 4.82% yield in a year

Math isn't my strong point but I think the rate is 4.738% equivalant.

I subtract $49414.72 (you Pay) from $50,000 (you get) and the profit is $585.28....since this is for 1/4 of the year...multiply $585.28 X 4 = $2,341.12 if it was for a year

take this $2,341.12 and devide it by your orginal investment $49,414.72 and multiply by 100 = 4.7377%

Hope this helps

50000=49414.72 e^r.3/12

rearranging and taking log on both sides,

r.3/12.log e = log(50000/49314.72)

Equivalent yield r =

= Log(50000/49314.72)x12/3=

=0.0552 = 5.52%