# Weird Present Value Formula?

Given: The bond equivalent yield of a 180-day banker’s acceptance quoted at a discount rate of 4.25% for a 360-day year is closest to

1. 4.31%.
2. 4.34%.
3. 4.40%.

My step for finding the PV of the Banker’s Acceptance is PV = 100 / [1 + (0.0425/2)] = 97.92

However, the solution gave: PV = FV × [1− (Days/Year)×DR] = 100 × [1−(180/360)×0.0425]

Could someone please explain why one would use the second formula? I’ve never seen it before :s

Thank you!

It’s a discount rate: you subtract the rate from 100% of the future value to get the present value.

You’re trying to treat it as an add-on rate: adding it to 100% of the present value to get the future value.

Thank you

You’re welcome.

I usually convert the bank discount yield (discount rate) to the actual dollar discount and work from there to calculate the holding period yield, then annualize to find the bond equivalent yield. So 4.25% * (180 / 360) = 2.125% discount from face value. HPY = (1000 / (1000 * (1-2.125%)) - 1) = 2.17%. Annualize this based on a 365-day year and simple interest only: 2.17% * (365 / 180) = 4.40%. Might take a bit more time but easier to remember then some non-intuitive formulas in my opinion.

What does HPY stand for?

HPY = Holding period yield