Change in discount - Amortization of Bonds

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Hello,
So I was wondering how the change in the discount between the interest and coupon in a certain period works towards reducing the total amoritization on a bond?
What is the intuition behind this?
Thank you!
 
FV = 67,831
PV = 65,584.35
Total discount = 2,246.64
First Year Interest Expense: 5,246.74
First Year Coupon Payment: 4,748.17
change in discount between interest and coupon = 498.5
Total discount - change in discount = amoritization after Year 1 = 1,748.07
I do not get the intuition behind the change in discount and how that fits into calculating amortization after Year 1
 
So the coupon rate is 7% and the YTM at issuance is 8%.
Each year the interest expense is the beginning-of-year balance times 8%.
Each year the coupon payment is $4,748.17.
The difference is the amortization, which is added to the beginning-of-year balance to get the end-of-year balance, which will be next year’s beginning-of-year balance.
You should make an amortization table in Excel; it will help you visualize what’s happening.
 
Coupon - Interest Component = Principal Component
This makes sense if the interest component is less than the coupon payments, but in this situation, where interest is actually greater than the entire coupon payment, this does not make as much sense to me. How does “negative principal” get paid off on a loan?
 
The initial Bonds Payable is less than the par value; you need to increase Bonds Payable over the life of the bonds.
You’re not paying off a loan here: the principal is paid 100% at maturity. What you’re doing is amortizing the premium or discount so that at maturity your liability is the par value that you’ll be paying off.
Once again, I encourage you to read the article I wrote on amortization tables and to create your own table (for this bond) in Excel. It will help your understanding immensely.
 
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