Lesson 1 of 4 11–14% of the exam

By Daniil Tarakanov Updated Oct 21, 20262027 curriculum

Bullet, amortizing and sinking fund bonds

A bullet bond pays only interest until maturity, then repays all the principal. Amortizing debt repays principal as it goes, fully (like a mortgage) or partially with a balloon at the end. Earlier principal means less credit risk for the investor, but more cash to reinvest at whatever rates prevail.

8 min cram, 36 min full read. Based on the 2027 CFA® Program Level I curriculum, Fixed Income, Learning Module 2. Also part of the 2026 curriculum, so it applies to the November 2026 exam too.

Tailor this to you: take the self-assessment

Before this: Fixed-Income Instrument Features, Time Value of Money in Finance

On the exam

Describe common cash flow structures of fixed-income instruments and contrast cash flow contingency provisions that benefit issuers and investors

Describe bullet, fully amortizing, partially amortizing, sinking fund and waterfall structures. Expect: which structure has the least credit risk or the most reinvestment risk; the level payment on an amortizing loan; the payment when a balloon is left at the end.

How deeply to learn each part

Know the idea: Understand it in general. It frames other topics, but you will not calculate with it.
Use it: Understand it well enough to solve a question with it. Recognize when it applies.
Memorize: Learn it by heart. The exam will not give it to you.

You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.

You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.

What is the difference between bullet and amortizing debt?

A bullet bond pays interest only until maturity and then returns all the principal in one go. Most government and corporate bonds are bullets, and investors like them because the stream and the maturity date are easy to match to a known future need.

Amortizing debt retires part of the principal before maturity, inside the regular payments. Mortgages and many loans work this way. A fully amortizing loan has level payments that leave a balance of zero at maturity. A partially amortizing bond has level payments too, but they leave part of the principal outstanding, which is repaid as a balloon payment with the final payment.

How principal comes back

Principal repayment structureswhen the investor gets the principal back

Bullet bond Memorize interest only; all principal at maturity
Amortizing debt Memorize principal repaid inside the payments
- Fully amortizing Memorize level payments; balance reaches zero at maturity
- Partially amortizing Memorize level payments, then a balloon payment at maturity
Sinking fund Memorize issuer retires part of the issue on a schedule
Waterfall Use it senior class gets principal first, junior class last

Borrowers like level payments because they match income that arrives evenly, such as rent for a landlord or salary for a household.

How do the structures change the investor’s risks?

The investor sits on the other side of the same cash flows, so two risks pull in opposite directions.

Credit risk is the chance the borrower cannot pay. It depends on how much principal is still outstanding, and amortizing debt shrinks that amount every period.
Reinvestment risk is the chance that cash returned early must be reinvested at lower rates than the bond pays. Amortizing debt returns more cash earlier, so there is more of it.

	Bullet	Partially amortizing	Fully amortizing
Principal outstanding over time	highest	middle	lowest
Investor’s credit risk	highest	middle	lowest
Reinvestment risk	lowest	middle	highest

Exam tip Think “cash back early”: less to lose, but more to re-lend. Never “safer in every way”.

How do you calculate the level payment?

The payments on a fully amortizing loan are an ordinary annuity whose present value is the amount borrowed. This is the annuity formula from the time value of money, with the payment as the unknown. Use the rate and the number of payments per payment period.

Level payment on an amortizing loan Memorize

A = \frac{r \times \text{Principal}}{1 - (1 + r)^{-N}}

Here r is the rate per period and N is the number of payments.

Worked example A EUR 80 million loan in seven annual payments

A lender advances EUR 80 million at 5% a year, repaid with seven equal annual payments.

Payment: A = 0.05 × 80 ÷ (1 − 1.05⁻⁷) = 4 ÷ 0.28932 = EUR 13.826 million.
Year 1 interest: 80 × 5% = 4.000. Principal repaid: 13.826 − 4.000 = 9.826. Balance: 70.174.
Year 2 interest: 70.174 × 5% = 3.509. Principal repaid: 10.317. Balance: 59.858.

The payment is fixed, so the interest share shrinks every year and the principal share grows. By year 7 the interest is only 0.658.

The payment on your calculator

2NDCLR TVM with P/Y set to 1
7N5I/Y80+|-PV
CPTPMT 13.83, or 13.8256 with more decimals shown

2ND second function (the shifted label above a key) · CLR TVM clear the time value of money keys · N number of periods · I/Y interest rate per year (per period when P/Y is 1) · +|- change sign · PV present value · CPT compute · PMT payment

fCLEAR FIN
7n5i80CHSPV
PMT 13.83, or 13.8256 with more decimals shown

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · CHS change sign · PV present value · PMT payment

Year 1 interest, to split the payment

80×0.05= 4

80ENTER0.05× 4

ENTER enter (on the HP, puts the number on the stack)

Rearrange itLevel payment: solve for payment, principal or number of payments

The question asks for

A loan of 80.00 at 5.00% per period is repaid in 7 equal payments. Each payment is closest to:

Principal (any units)Rate per period%Number of payments, N

A = \frac{r \times Principal}{1 - ( 1 + r ) ^{- N}}

0.05 × 80.00 ÷ (1 − 1.05^−7) = 13.83

Payment each period (same units as principal)13.83

On your calculator

2NDCLR TVMwith P/Y set to 1
7N5I/Y80+|-PV
CPTPMTpositive: the lender receives it

fCLEAR FIN
7n5i80CHSPV
PMTpositive: the lender receives it

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · CHS change sign · PV present value · PMT payment

InteractiveBullet, partially or fully amortizing: same loan, different cash flows

Try this 0 of 3

Switch the worked loan to a bullet and compare the principal still owed
Make it partially amortizing with a EUR 25m balloon
Load the monthly mortgage and read the first month's split

Annual rate5%

Term (years)7 years

Payment each yearEUR 13.826m

Last paymentEUR 13.826m

Total interestEUR 16.779m

Interest (hatched)
Principal repaid
Principal outstanding

First year: interestEUR 4.000m

First year: principalEUR 9.826m

Average principal outstandingEUR 47.940m

Fully amortizing: principal comes back with every payment and nothing is left at maturity. Least credit risk, most cash to reinvest.

Show working

Periodic rate r = 5% ÷ 1 = 5%; payments N = 7 × 1 = 7.

A = r × Principal ÷ [1 − (1 + r)^−N] = 0.05 × 80 ÷ [1 − 1.05⁻⁷] = EUR 13.826m

First year: interest 80 × 0.05 = EUR 4.000m; principal EUR 9.826m; still owed EUR 70.174m.

On your calculator

2NDCLR TVMwith P/Y set to 1
7N5I/Y80+|-PV0FV
CPTPMT13.826

fCLEAR FIN
7n5i80CHSPV0FV
PMT13.826

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · CHS change sign · PV present value · FV future value · PMT payment

Same loan, same rate: paying principal earlier cuts credit risk but hands you more cash to reinvest.

The money is entered from the lender’s side: the loan goes out (negative PV) and the payments come back (positive PMT). On a monthly loan, divide the annual rate by 12 and multiply the years by 12. A USD 300,000 mortgage at 6% over 25 years has r = 0.5% and N = 300, which gives a payment of USD 1,932.90, of which the first month’s interest is USD 1,500.

Worked example A partially amortizing version

Same loan, but EUR 25 million is left to repay at maturity.

Present value of the balloon: 25 ÷ 1.05⁷ = 17.767.
Amount to amortize with the level payments: 80 − 17.767 = 62.233.
Payment: 0.05 × 62.233 ÷ (1 − 1.05⁻⁷) = EUR 10.755 million a year, plus the EUR 25 million balloon at the end.

The payment is smaller than the 13.826 on the fully amortizing loan, so the principal outstanding stays higher and so does the credit risk.

The payment with a balloon

2NDCLR TVM with P/Y set to 1
7N5I/Y80+|-PV25FV
CPTPMT 10.76, or 10.7551 with more decimals shown

fCLEAR FIN
7n5i80CHSPV25FV
PMT 10.76, or 10.7551 with more decimals shown

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · CHS change sign · PV present value · FV future value · PMT payment

Payment when a balloon is left at maturity Use it

A = \frac{r \times \left[\text{Principal} - B(1 + r)^{-N}\right]}{1 - (1 + r)^{-N}}

B is the balloon. On the calculator you never need this form: put the balloon in FV, the future value.

Rearrange itBalloon loan: solve for the payment or the balloon

The question asks for

A loan of 80.00 at 5.00% per period is repaid with 7 equal payments and a balloon of 25.00 at the end, on top of the last payment. Each regular payment is closest to:

Principal (any units)Balloon repaid at maturity (same units)Rate per period%Number of payments, N

A = \frac{r \times [ Principal - B ( 1 + r ) ^{- N} ]}{1 - ( 1 + r ) ^{- N}}

0.05 × (80.00 − 25.00 ÷ 1.05^7) ÷ (1 − 1.05^−7) = 10.76

Payment each period (same units)10.76

On your calculator

2NDCLR TVMwith P/Y set to 1
7N5I/Y80+|-PV25FV
CPTPMT

fCLEAR FIN
7n5i80CHSPV25FV
PMT

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · CHS change sign · PV present value · FV future value · PMT payment

What are sinking funds and waterfalls?

Both are ways of retiring principal early or in an agreed order.

A sinking fund is the issuer’s plan to retire a bond’s principal on a schedule. The issuer may direct the trustee to redeem a set amount of bonds chosen at random, or it may buy bonds back at a fixed price. Like amortization, it lowers credit risk and raises reinvestment risk, because principal outstanding falls before maturity.

Waterfall structures serve investors with different claims on one pool of cash flows, such as the loans behind an asset-backed security. Interest goes to all classes. Principal is repaid in order: the most senior class first, then the next, and so on. Any shortfall lands on the most junior class first, so the senior class has the lowest credit risk. The detail belongs to the securitization modules.

Go deeper A partially amortizing bond is a loan plus a zero

The same bond can be split in two: a fully amortizing loan on part of the principal, plus a single payment at maturity for the balloon. The price is the sum of the two present values. That is exactly the calculation above: the balloon’s present value is taken off first, and the rest is amortized.

Go deeper Why an issuer might buy sinking fund bonds in the market

If the bonds trade below the price at which the sinking fund can redeem them, the issuer can retire its obligation more cheaply by buying them in the open market. If they trade above, it uses the redemption right at the fixed price. The investor whose bond is picked at random gets the fixed price, which can be better or worse than the market.

Memorize this

MemorizePrincipal structures and the two risks

	Bullet	Partially amortizing	Fully amortizing
Principal outstanding	highest	middle	lowest
Credit risk	highest	middle	lowest
Reinvestment risk	lowest	middle	highest

Memory hook Less principal outstanding means less to lose, but more cash coming back early that must be re-lent: credit risk and reinvestment risk move in opposite directions.

Know it cold More amortization: less credit risk, more reinvestment risk. Sinking funds work the same way.

MemorizeLevel payment

Memory hook It is the TVM annuity: PV = principal, N payments, solve for PMT.

Know it cold $A = \dfrac{r \times \text{Principal}}{1 - (1 + r)^{-N}}$ with $r$ and $N$ per payment period (monthly loan: divide the rate by 12, multiply the years by 12).

MemorizeWaterfall

Memory hook Water runs down: principal pays the top class first; losses climb up from the bottom.

Know it cold Interest goes to all classes. Principal goes most senior first. Losses hit the most junior first.

How principal comes back

Principal repayment structureswhen the investor gets the principal back

Bullet bond Memorize interest only; all principal at maturity
Amortizing debt Memorize principal repaid inside the payments
- Fully amortizing Memorize level payments; balance reaches zero at maturity
- Partially amortizing Memorize level payments, then a balloon payment at maturity
Sinking fund Memorize issuer retires part of the issue on a schedule
Waterfall Use it senior class gets principal first, junior class last

Level payment on an amortizing loan

A = \frac{r \times \text{Principal}}{1 - (1 + r)^{-N}}

Quick example

GBP 1,200,000 at 3% a year, three equal annual payments. 0.03 × 1,200,000 ÷ (1 − 1.03⁻³) = GBP 424,236.

On your calculator

2NDCLR TVM with P/Y set to 1
3N3I/Y1200000+|-PV
CPTPMT 424,236.44

fCLEAR FIN
3n3i1200000CHSPV
PMT 424,236.44

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · CHS change sign · PV present value · PMT payment

Payment when a balloon is left at maturity

A = \frac{r \times \left[\text{Principal} - B(1 + r)^{-N}\right]}{1 - (1 + r)^{-N}}

Quick example

EUR 80 million at 5% a year, seven annual payments, EUR 25 million balloon at the end. EUR 10.755 million a year.

On your calculator

2NDCLR TVM with P/Y set to 1
7N5I/Y80+|-PV25FV
CPTPMT 10.7551

fCLEAR FIN
7n5i80CHSPV25FV
PMT 10.7551 (with four decimals shown)

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · CHS change sign · PV present value · FV future value · PMT payment

How it is asked

Which structure has the most or the least of a risk?

Compared with a bullet bond, a fully amortizing bond exposes the investor to what?

Less credit risk, more reinvestment risk. Trap: "less of both".
Level payment

GBP 1,200,000 at 3%, three equal annual payments. Payment?

PMT with N = 3, I/Y = 3, PV = −1,200,000: GBP 424,236. Trap: 400,000 (principal ÷ 3) or 436,000 (400,000 + first-year interest of 36,000).
Balloon loan

Same loan, but GBP 250,000 is left as a balloon. Payment?

Enter the balloon as FV, solve PMT. The payment is lower than the fully amortizing one.
Who is paid first, who absorbs losses?

In a sequential-pay waterfall, which class receives principal first?

The most senior class. Losses go to the most junior class.

Exam traps

Saying amortizing debt has less reinvestment risk. It has more: the cash comes back early and must be reinvested at whatever rates prevail.
Dividing principal by N and adding the first period's interest. That is an equal-principal schedule, not a level payment.
Forgetting to convert the annual rate and the term to periodic values on a monthly loan: use r ÷ 12 and N × 12.
Treating the balloon as extra to be amortized. It is repaid at maturity, so the regular payments are smaller than on a fully amortizing loan.

Checkpoint

4 exam-style questions. About 90 seconds each.

1A CHF 2,000,000 loan at 4% a year is repaid with four equal annual payments. Each payment is closest to:
2Compared with an otherwise identical bullet bond, a fully amortizing bond most likely exposes the investor to:
3In a sequential-pay waterfall, the class that receives principal first is the class that:
4A EUR 60 million loan at 6% a year is repaid with five equal annual payments, plus a EUR 20 million balloon payment at the end of year 5 on top of the last payment. Each regular payment is closest to:

Key takeaways

Bullet: interest only, all principal at maturity. Amortizing: principal comes back inside the payments.
More amortization means less credit risk and more reinvestment risk.
Level payment A = r × Principal ÷ [1 − (1 + r)^−N]; interest shrinks and principal grows while the payment stays fixed.
A partially amortizing bond is a fully amortizing loan on part of the principal plus a balloon at maturity.
Sinking funds retire principal on a schedule; waterfalls repay principal to the most senior class first.

Level payment on an amortizing loan

A = \frac{r \times \text{Principal}}{1 - (1 + r)^{-N}}

Quick example

GBP 1,200,000 at 3% a year, three equal annual payments. 0.03 × 1,200,000 ÷ (1 − 1.03⁻³) = GBP 424,236.

On your calculator

2NDCLR TVM with P/Y set to 1
3N3I/Y1200000+|-PV
CPTPMT 424,236.44

fCLEAR FIN
3n3i1200000CHSPV
PMT 424,236.44

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · CHS change sign · PV present value · PMT payment

Payment when a balloon is left at maturity

A = \frac{r \times \left[\text{Principal} - B(1 + r)^{-N}\right]}{1 - (1 + r)^{-N}}

Quick example

EUR 80 million at 5% a year, seven annual payments, EUR 25 million balloon at the end. EUR 10.755 million a year.

On your calculator

2NDCLR TVM with P/Y set to 1
7N5I/Y80+|-PV25FV
CPTPMT 10.7551

fCLEAR FIN
7n5i80CHSPV25FV
PMT 10.7551 (with four decimals shown)

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · CHS change sign · PV present value · FV future value · PMT payment

All Fixed Income formulas, every lesson

Practice exam-style questions on Fixed-Income Cash Flows and Types

Next lesson Floating, step-up, inflation-linked and zero-coupon bonds

Questions about this lesson?

Where this comes back

Bond Valuation: Prices and Yields Fixed Income
Mortgage-Backed Securities: RMBS, CMOs and CMBS Fixed Income
Asset-Backed Securities, Covered Bonds and CDOs Fixed Income

Questions candidates ask

What is the difference between a bullet bond and an amortizing bond?

A bullet bond pays interest only and repays all principal at maturity. An amortizing bond repays part of the principal in every payment, so the amount owed shrinks over time and credit risk falls.

What is a balloon payment?

The principal left to repay at maturity on a partially amortizing bond or loan. It is paid together with the final regular payment, and it makes the regular payments smaller than on a fully amortizing loan.

How does a sinking fund work?

The issuer retires part of the bond issue on a schedule before maturity. It either redeems bonds picked at random at a set price or buys them back, so less principal is outstanding as time passes.

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