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Lesson 1 of 7 · 14 min

Bullet, fully amortizing and partially amortizing bonds

A bullet bond pays only interest until it returns all principal at maturity, an amortizing bond returns principal along the way with a level payment, and a partially amortizing bond does a bit of both by leaving a balloon at the end.

Video lesson · 5 min. Watch it first, then use the text below to go deeper.

In short

Bullet bond: fixed coupons that are interest only; the whole principal comes back with the last coupon.
Fully amortizing: a level periodic payment of interest plus principal that brings the balance to zero at maturity (mortgages are the classic case).
Partially amortizing: level payments repay part of the principal; the rest is a balloon payment at maturity.
Level payment: $A = \dfrac{r \times \text{Principal}}{1-(1+r)^{-N}}$ . Inside it, interest shrinks and principal grows each period.
Earlier principal repayment means lower credit risk but higher reinvestment risk for the investor.

The bullet bond: interest now, principal later

The standard structure is the bullet bond. The issuer receives the principal at settlement, pays a fixed coupon every period, and repays the full principal together with the final coupon. Most government and corporate bonds look like this.

Every coupon is pure interest, because no principal is repaid until the end. Investors like the predictable income and the known maturity date, which helps them fund known future liabilities.

The drawback is concentration: the investor's biggest cash flow arrives on one date at the very end. If the issuer's finances weaken in the meantime, the entire principal is still at risk.

EUR 200m at 4% semiannual for 4 years as a bullet (half-years on the axis): seven small coupons of pure interest, then all the principal at once with the last coupon. That single large final flow is the investor's concentration of credit risk.

Fully amortizing: one level payment that does two jobs

A fully amortizing instrument retires principal from the first payment date onward. The borrower pays the same amount A every period. Each A first covers interest on the balance still outstanding, and whatever is left over reduces that balance.

Because the balance falls every period, the interest part of A falls too, so the principal part grows. Early payments are mostly interest; late payments are mostly principal. The last payment brings the balance exactly to zero.

Mortgage loans are the textbook example. Households and property owners like a constant payment because it matches a salary or a stream of rental income. In some markets these loans are pooled into mortgage-backed securities whose cash flows look the same.

Corvella Rail's fully amortizing loan: every payment is the same 27.302, but the interest slice shrinks from 4.000 to 0.535 as the balance falls, so the principal slice grows each period.

The first interest payment of a fully amortizing loan equals the first coupon of a bullet bond with the same principal and rate. The two structures only diverge after the first principal repayment.

Partially amortizing: level payments plus a balloon

A partially amortizing bond amortizes only part of the principal through level payments and repays the remainder as a lump sum, the balloon payment, at maturity. It sits between the bullet bond (balloon = 100% of principal) and the fully amortizing loan (balloon = 0).

The easiest way to price the level payment is to split the bond in two: (1) the balloon, whose present value is $\text{Balloon}/(1+r)^N$ , and (2) a fully amortizing loan on the rest. Subtract the balloon's PV from the principal, then apply the annuity formula to what remains.

An equivalent view: the payment equals interest on the balloon every period plus a fully amortizing payment on the non-balloon part. Either way, the outstanding balance stays higher than in a fully amortizing loan, so each interest payment after the first is larger.

Three ways to repay EUR 200m at 4% (semiannual), 4 years (Example 1–2 numbers)
Feature	Bullet	Partially amortizing (balloon 100)	Fully amortizing
Payment, periods 1–7	4.000	15.651	27.302
Final payment	204.000	115.651	27.302
Principal outstanding before final payment	200.0	113.4	26.8
Credit risk to investor	Highest	Middle	Lowest
Reinvestment risk to investor	Lowest	Middle	Highest

Principal outstanding after each payment on Corvella's EUR 200m. The partially amortizing bond sits between the other two and still owes the 100 balloon at the end; the higher the line, the more is exposed to default, but the less cash comes back early to reinvest.

What the investor gains and gives up

Amortization gives investors higher near-term cash flows and lower credit risk, because the amount the borrower still owes falls over time. Less money is exposed to a default late in the bond's life.

The price is reinvestment risk. The investor receives larger amounts early and must reinvest them at whatever rates prevail then, which may be lower. The more principal comes back early, the bigger this effect: it is largest for a fully amortizing loan and smallest for a bullet bond.

So an investor who worries more about the issuer's credit than about reinvestment rates prefers amortizing debt; one who wants to lock in a rate for the full term prefers a bullet.

Formulas

Level payment on a fully amortizing loan: $A = \dfrac{r \times \text{Principal}}{1-(1+r)^{-N}}$
r = market rate per period, N = number of payments. Same as solving for PMT on the calculator with FV = 0.
Interest and principal in each payment: $\text{Interest}_t = r \times \text{Balance}_{t-1}, \quad \text{Principal}_t = A - \text{Interest}_t$
New balance = old balance − principal repaid. Interest falls and principal rises each period.
Partially amortizing payment: $A = \dfrac{r \times \left(\text{Principal} - \dfrac{\text{Balloon}}{(1+r)^N}\right)}{1-(1+r)^{-N}}$
Amortize only the principal minus the PV of the balloon; the balloon is paid on top of the last A.

Worked examples

Example 1 Fully amortizing schedule

Corvella Rail borrows EUR 200 million for 4 years at 4.0% a year, paid semiannually, fully amortizing. What is the level payment, and how is the first and second payment split between interest and principal?

Example 2 Adding a balloon

Corvella Rail instead issues a 4-year, 4.0% semiannual partially amortizing bond on EUR 200 million that leaves a EUR 100 million balloon at maturity. What is the level payment, and what does the investor receive at maturity?

Example 3 Monthly mortgage loan

A household borrows NOK 3,000,000 over 25 years at 4.8% a year with monthly payments, fully amortizing. What is the monthly payment, and how much of the first payment is principal?

On the exam

Expect a level-payment calculation (sometimes asking for the interest or principal part of the first payment) and concept items comparing credit and reinvestment risk across bullet, partially and fully amortizing structures.

Forgetting to convert the rate and N to the payment frequency (semiannual or monthly).
Amortizing the full principal of a partially amortizing bond. Only principal minus the PV of the balloon is amortized.
Saying amortizing debt has lower reinvestment risk. It has lower credit risk but higher reinvestment risk.
Assuming the principal portion is constant. The payment is constant; the principal portion grows.

Check yourself

Q1A USD 5,000,000 fully amortizing loan carries 6% interest with 5 annual payments. The annual payment is closest to:
Q2For the loan in the previous question, the principal repaid with the first payment is closest to:
Q3A EUR 10m, 4-year, 5% annual-pay partially amortizing bond leaves a EUR 4m balloon at maturity. The level annual payment (excluding the balloon) is closest to:
Q4Compared with an otherwise identical bullet bond, a fully amortizing bond most likely exposes the investor to:
Q5Three bonds with the same principal, rate and maturity are bullet, partially amortizing and fully amortizing. Their first-period interest payments are:

0/5Check yourself

Answer the 5 questions: +10 XP for each one you get right first time.

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