I understand that when a discount bond is issued, there’s an amortization of the discount. However, could someone explain how the interest expense increases over time to reach par at maturity? Why does occur? I am trying to understand it more conceptually

You’re amortizing the discount based on the original YTM: to get the interest expense each period you multiply the YTM by the beginning liability (= par – remaining discount). Because the beginning liability increases each period (i.e., the discount gets smaller each period), the interest expense increases each period.

I’d encourage you to make an amortization table in Excel so that you can see how the numbers change; it will be quite enlightening. I wrote an article on amortization tables that may be of some help: http://financialexamhelp123.com/amortization-tables/.

An easy way to think about this is if you consider a zero coupon bond. Lets say a 2 year bond with a yield to maturity of 10%:

When the bond is sold it is worth: 100 / 1.10 ^ 2 = $82.64

The first year, the bond appreciates:

$82.64 * 10% = $8.264 and is worth $90.91 at the end of year 1

In the second year the bond appreciates:

$90.91 * 10% = $9.091 and is worth $100 at the end of year 2

So in the first year, the bonds interest expense is $8.264 and in the second year the bonds interest expense is $9.091, even though over the life of the bond the investor earned 10% per annum.