Present Value of Expected Loss

Hi,

I am having troubles calculating PV of expected loss on a bond. Please refer to example 8 in the curriculum (FI book) page 286.

I have no problem calculating PV of expected loss on a single payment (part 1,2 and 3 of the example).

I am facing problems in calculating PV of expected loss on a bond (Part 4 and 5). It will be very time consuming to to caluclate PV of expected loss at each maturity and then sum up and then take the difference…

I tried to figure a way to solve with the calc but i couldnt because the discounting is continuous.

The question shows 2 formulas in the beginning of part 4, value of bond at time t and value of bond if it was risk free, i dont understand these forumlas.

The LOS says: Calculate and interepret PV of expected loss on a bond given a time horizon.

Help is appreciated!