Question 11 A $100 notional, zero coupon bond has one year to expiry. The probability of default is 10%. In the event of default, assume that the recovery rate is 40%. The continuously compounded discount rate is 5%. What is the present value of this bond? Answer for PV: e^-0.05 * 94 = 89.42

1) I understand that future value is expected value etc, but I don't recall the basic PV formula consisting of the exponential. Is this an exception when looking at bond returns?

2) How much should we pay attend to Miller's end of chapter practice questions? They are much simpler in nature to BT's but seem to be concept driven (e.g. proofs) and calculation heavy (calculating means and variances with >4 inputs). Slightly related to this, I was reading another thread that knowledge of calculus is not expected, however a lot of the Miller and BT questions result in calculation of integral of pdf?

Thank you!