CFA Level I Exam · Fixed-Income Cash Flows and Types

Principal Repayment Structures: Bullet, Amortizing and Sinking Fund

Updated 7 October 2026 · Fact-checked

A principal repayment structure sets when a borrower pays back the amount borrowed. A bullet bond repays all principal at maturity. An amortizing bond repays principal over time. A partially amortizing bond leaves a balloon payment. A sinking fund retires bonds early. To solve questions, list each period's cash flows and track the balance.

Understand Principal Repayment Structures

Every bond or loan has two cash flow parts: interest and principal. The principal repayment structure tells you how and when the principal comes back to the lender. This changes the size of each payment, the remaining balance, and the risk the lender faces.

In a bullet structure, the borrower pays only interest until maturity, then repays the full principal in one payment. Most plain corporate and government bonds work this way. All the credit risk sits at the end.

In an amortizing structure, each payment includes both interest and some principal. In a fully amortizing loan, level payments reduce the balance to zero by maturity. Early payments are mostly interest; later payments are mostly principal. In a partially amortizing loan, payments do not cover the full principal, so a lump sum called a balloon payment is due at maturity. A bullet bond is the extreme case with zero amortization during the term.

A sinking fund provision requires the issuer to retire part of the issue on a schedule, either by calling bonds at a set price (often par) or buying them in the market. It lowers credit risk because the debt shrinks before maturity. The cost to investors is reinvestment risk: your bond may be retired early. Sinking fund terms can vary, such as a fixed schedule or a larger repayment option for the issuer.

A waterfall structure appears in securitization. Cash from a pool of loans is paid to tranches in order of priority. Senior tranches receive principal and interest first; junior tranches absorb shortfalls. So the principal repayment depends on the pool's cash flow and the tranche's rank, not on one fixed schedule.

Key formulas to remember

Interest in a period: Interest = beginning balance × periodic rate; Use the rate per period. For semiannual payments, divide the annual rate by 2.
Principal repaid in a payment: Principal repaid = payment − interest; For a fully amortizing loan, the principal portions sum to the original principal.
Ending balance: Ending balance = beginning balance − principal repaid; Next period's interest is based on this balance.
Level payment (fully amortizing): Payment = PV × r ÷ [1 − (1 + r)^−n]; r is the rate per period and n the number of periods. On a calculator, use PV, N, I/Y and CPT PMT.
Balloon payment: Balloon = remaining balance after the last regular payment; Equals the future value of the loan less the future value of the payments made.
Bullet bond cash flows: Coupons = rate × principal each period; principal repaid once at maturity; No amortization before maturity.

How to solve Principal Repayment Structures questions

Use this method for any question on repayment structures. Most errors come from skipping the balance tracking.

1Identify the structure: bullet, fully amortizing, partially amortizing with balloon, sinking fund or waterfall.
2Write down the principal, the rate per period and the number of periods.
3Find the regular payment if it is not given. Use the level payment formula or the calculator.
4For each period, compute interest = beginning balance × rate.
5Subtract interest from the payment to get principal repaid, then update the balance.
6For a balloon, take the balance after the final regular payment as the lump sum due.
7For a sinking fund, reduce the outstanding principal by the amount retired each year and recompute interest on the lower balance.
8Check the answer: a fully amortizing balance ends at zero, and total principal repaid equals the original principal.

Quickest way: Compare structures by the shape of cash flows

When to use it: Use this for conceptual questions where you need to pick between structures or compare risk, not compute a full schedule.

Ask: is principal returned before maturity? If no, it is bullet.
If yes, does the balance reach zero at maturity? If yes, fully amortizing. If a lump sum remains, partially amortizing with a balloon.
Remember that amortizing debt has lower overall credit exposure and a shorter weighted average life than a bullet bond of the same maturity.
Interest in a level-payment loan falls each period, and principal rises, so the first interest amount is the largest.
Spot the sinking fund wording: it means scheduled early retirement, lower credit risk, and higher reinvestment risk for the holder.

Common mistakes in Principal Repayment Structures

Treating a balloon payment as an extra payment on top of full repayment.
The word suggests something added, so students forget it is the unpaid principal.
Fix: The balloon is the remaining balance due at maturity. Regular payments plus the balloon repay the loan.
Computing interest on the original principal in every period of an amortizing loan.
Students copy the bullet approach.
Fix: Always use the beginning balance of that period. Interest falls as the balance falls.
Using the annual rate with monthly or semiannual payments.
The rate is quoted annually and students skip the conversion.
Fix: Divide the annual rate by payments per year and multiply the years by payments per year.
Thinking a sinking fund always benefits the bondholder.
It lowers default risk, so it looks purely positive.
Fix: It also creates reinvestment risk, since bonds may be retired early, often at par even if the bond trades above par.
Assuming the principal part of a level payment is constant.
The total payment is constant, so students assume its parts are too.
Fix: In a level-payment loan, the interest part falls and the principal part rises each period.
Confusing waterfall with sinking fund.
Both involve scheduled or ordered principal payments.
Fix: A sinking fund is an issuer's schedule to retire its own debt. A waterfall is a priority order for distributing pool cash among tranches.

Worked examples

Example 1

A 3-year loan of USD 100,000 is fully amortizing with annual payments at 10%. The annual payment is USD 40,211. What principal is repaid in year 2? A. USD 30,211 B. USD 33,232 C. USD 36,556

Show the solution

Year 1 interest = 100,000 × 10% = 10,000.
Year 1 principal = 40,211 − 10,000 = 30,211. Balance = 100,000 − 30,211 = 69,789.
Year 2 interest = 69,789 × 10% = 6,978.9.
Year 2 principal = 40,211 − 6,978.9 = 33,232.1.
Balance after year 2 = 69,789 − 33,232.1 = 36,556.9.
Check with year 3: interest = 36,556.9 × 10% = 3,655.69, so principal = 40,211 − 3,655.69 = 36,555.31. The balance after year 3 is 36,556.9 − 36,555.31 = about 1.6, a small rounding difference because the payment of 40,211 is rounded (the unrounded payment is about 40,211.48). The schedule closes.

Answer: B. USD 33,232

Example 2

A 5-year loan of EUR 200,000 pays 6% interest annually and is partially amortizing. The borrower repays EUR 20,000 of principal at the end of each of years 1 to 5, plus interest on the beginning balance. The principal still outstanding after the year 5 regular payment is due as a balloon at the end of year 5, in addition to the year 5 regular payment. What is the balloon payment? A. EUR 100,000 B. EUR 120,000 C. EUR 180,000

Show the solution

Principal repaid through regular payments in years 1 to 5 = 5 × 20,000 = 100,000.
Balance remaining after the year 5 regular payment = 200,000 − 100,000 = 100,000. This is the balloon.
Check with year 5: the beginning-of-year-5 balance is 200,000 − 4 × 20,000 = 120,000. Year 5 interest = 120,000 × 6% = 7,200, so the year 5 regular payment is 20,000 + 7,200 = 27,200.
After that payment the balance is 120,000 − 20,000 = 100,000, which is due as the balloon at the end of year 5, together with the year 5 regular payment. The interest figure does not change the balloon.
Option B (120,000) is a trap: it is the balance at the start of year 5, before that year's principal payment.

Answer: A. EUR 100,000

Exam tips

Questions give three options listed from smallest to largest. Estimate the balance first, then eliminate options that are clearly too large or too small.
Know the direction of change: in a level-payment loan, interest falls and principal rises each period. Many conceptual items test only this.
Read whether the question asks for the payment, the principal portion, the interest portion or the balance. They differ.
With a calculator, set payments per year to 1 and use CPT PMT on the TI BA II Plus: enter N, I/Y, PV, then CPT PMT. The result is negative for a positive PV.
For sinking funds, link the answer to risk: lower credit risk, higher reinvestment risk, shorter average life.

Practice questions from Fixed-Income Cash Flows and Types

Principal Repayment Structures: frequently asked questions

What is the difference between fully amortizing and partially amortizing bonds?

A fully amortizing bond repays all principal through its regular payments, so the balance is zero at maturity. A partially amortizing bond repays only some principal, so a balloon payment is due at maturity.

How does a bullet bond differ from an amortizing bond?

A bullet bond pays only interest until maturity and repays all principal at the end. An amortizing bond includes principal in each payment. Compared with a bullet bond of the same maturity, amortizing debt has lower overall credit exposure and a shorter weighted average life.

What is a sinking fund provision?

It requires the issuer to retire part of the bond issue before maturity, either by calling bonds at a set price or buying them in the market. It reduces credit risk but gives investors reinvestment risk.

How do I build an amortization schedule for the exam?

Find the level payment, then for each period compute interest on the beginning balance, subtract it from the payment to get principal, and reduce the balance. Repeat until the balance reaches zero or the balloon amount.