Why the discount cannot just sit there
The previous guide left you with a small mystery. A company issued bonds with a face value of 100,000 but, because its printed coupon rate was a little below what the market demanded, investors only handed over 96,000 in cash. The 4,000 shortfall is the bond discount. On the issue date the balance sheet shows bonds payable of 100,000 reduced by an unamortized discount of 4,000, so the net amount the company really owes — its carrying value — is 96,000. But that carrying value cannot stay at 96,000 forever, because on the maturity date the company must repay the full 100,000 of face. Somewhere across the bond's life, that 4,000 gap has to close.
Closing that gap, a little each period, is what amortizing the discount means. And there is a deeper reason it must happen than just "the numbers have to line up at the end." Think about what the company really paid to borrow. It received 96,000 today, it will pay back 100,000 at maturity, and along the way it also pays cash coupons. The extra 4,000 it repays beyond what it borrowed is a genuine cost of borrowing — interest, in substance, even though it is never labelled as a coupon. Honest accounting refuses to let that 4,000 vanish; it spreads it across the life of the loan as added interest expense, year by year, so each period bears its fair share of the true cost of the debt.
A premium is the same story told in a mirror. If the coupon had been a touch above what the market wanted, eager investors would have paid 104,000 for the same 100,000 bond. The extra 4,000 they overpaid is the bond premium, and it works in the company's favour: it borrowed 104,000 but only repays 100,000, so the premium is a reduction of its borrowing cost. Amortizing a premium therefore *lowers* interest expense over time, again until carrying value lands precisely on face at maturity. Discount pulls carrying value up toward face; premium pulls it down toward face. Either way, both roads end at the same place: 100,000.
Interest expense is not the cash you pay
Here is the single most important idea in this guide, and a place beginners stumble badly: the cash coupon you pay and the interest expense you record are two different numbers. The cash coupon is fixed and dull — it is always the face value times the coupon rate. On our 100,000 bond with a 5 percent coupon paid annually, the company hands bondholders exactly 5,000 every year, no matter what. That number never moves. It is printed on the bond and it does not care what investors paid or what carrying value is today.
Interest expense is the truer number, and it is bigger than the cash coupon whenever there is a discount. Why bigger? Because the company is not just paying 5,000 of cash this year — it is also burning through a slice of that 4,000 discount, which is itself extra interest it owes. So expense equals the cash coupon plus the amortized chunk of discount. The difference between the two is exactly the amount of discount used up this period, and that difference is what raises carrying value. With a premium it flips: expense is *less* than the cash coupon, because part of each 5,000 you pay is really returning the bondholders' own overpayment rather than compensating them for the loan.
The effective-interest method, step by step
Now, how much of the discount do we amortize each period? US GAAP requires the effective-interest method, and its logic is beautiful once you see it. Recall the present value idea from earlier in this rung: investors paid 96,000 because, at the market's required yield, that is what the bond's future cash flows are worth today. Call that yield the effective rate — suppose it is about 6 percent. The method says: each period, the true interest expense is the effective rate applied to the *carrying value at the start of the period*. That is the heart of it, and everything else falls out.
- Interest expense = beginning carrying value x effective rate. Year 1: 96,000 x 6% = 5,760.
- Cash coupon = face value x coupon rate. Always 100,000 x 5% = 5,000.
- Discount amortized this period = expense - cash coupon = 5,760 - 5,000 = 760.
- New carrying value = old carrying value + discount amortized = 96,000 + 760 = 96,760. Repeat next year using 96,760 as the new starting point.
Notice the lovely self-correcting motion. Because carrying value rises each year, next year's expense (6 percent of a bigger base) is a touch larger, so the amortized slice grows a little too. The discount melts away faster and faster, and the carrying value accelerates toward 100,000, arriving exactly there in the final period. The bond pulls itself home. This is also why the method is called *effective-interest amortization*: the expense always reflects the real economic yield on the money actually owed at that moment, not a number plucked from the air.
Effective rate 6% | Cash coupon fixed at 5,000 (100,000 x 5%) Year Begin CV Expense(6%) Cash Amort. End CV 1 96,000 5,760 5,000 760 96,760 2 96,760 5,806 5,000 806 97,566 3 97,566 5,854 5,000 854 98,420 ... ... ... ... ... ... last ~ ~5,943 5,000 ~943 100,000 <- lands on face Expense > Cash every year (discount) -> CV climbs to face Each year's Amort = Expense - Cash, and it gets a little bigger
The journal entry, and the straight-line shortcut
With the schedule in hand, the period-end journal entry almost writes itself, and it carries three numbers from a single row. You debit interest expense for the true expense (5,760), you credit cash for the fixed coupon you actually pay (5,000), and you credit the discount account for the slice amortized (760). The debits and credits balance, because 5,760 equals 5,000 plus 760. Crediting the discount is the subtle move: the discount is a *contra* to bonds payable, so shrinking it by 760 raises the net carrying value by exactly that much — the climb toward face happens automatically, no separate entry needed.
For a premium, the same row gives the mirror entry: you still credit cash 5,000, but now expense is *smaller* (say 4,800), so to make the entry balance you must also debit the premium account for 200. Debiting the premium shrinks it, which lowers carrying value toward face. The mechanical tell is simple and worth memorizing: with a discount you *credit* the discount each period; with a premium you *debit* the premium each period. In both cases the contra-or-adjunct account marches steadily to zero by maturity, leaving bonds payable standing cleanly at 100,000, ready to be repaid.
There is a simpler cousin to all this called straight-line amortization: just divide the total discount evenly across the periods. With our 4,000 discount over, say, five years, you would amortize a flat 800 every single year — no schedule, no rising slices. It is easier, and US GAAP *permits* it, but only when the result is not materially different from the effective-interest method. Straight-line is honest enough for a small, short bond where the difference is pennies; it quietly distorts the picture for a large, long one, because it pretends the company's interest expense is constant when its real cost of debt rises as carrying value climbs. So treat straight-line as a convenience the rules tolerate, not the principle they prefer.
Two honest cautions before you move on
First, do not confuse carrying value with market value. Amortization marches carrying value along a fixed, pre-computed path toward face, utterly indifferent to what is happening in the world. But the bond's actual market price bounces around daily as interest rates move: if rates rise after issue, the bond trades for less than its carrying value; if rates fall, more. Book value is a disciplined accounting story about the original deal; market value is what a buyer would pay today. They coincide only by accident. This is the same book-value-is-not-market-value lesson the asset rungs taught you, now wearing a liability's clothes.
Second, the very same machinery runs on the investor's side of the deal — it is just mirrored. Where the issuer records bonds payable and interest expense, the buyer holds a bond investment and records interest revenue, amortizing the discount or premium to pull *their* carrying value toward face. You have already glimpsed this logic with interest on notes receivable: effective-interest amortization is the universal grammar for any debt instrument bought or sold away from its face. Learn it once here and you have learned both sides forever.