What is an amortized bond (brief definition)
– An amortized bond is a debt contract in which the issuer repays portions of the principal (face value) over the life of the instrument instead of returning the entire principal only at maturity. Each scheduled payment typically includes both interest and principal.
Key terms (defined)
– Amortization schedule: a table that breaks each payment into interest and principal and shows the remaining balance after each period.
– Bond discount / premium: a discount occurs when a bond is sold for less than face value; a premium occurs when it is sold for more. The difference is often amortized for accounting and tax purposes.
– Straight-line method: an accounting approach that spreads the total discount (or premium) equally across periods.
– Effective-interest method (also called the market-interest or yield method): an accounting approach that allocates amortization so that interest expense each period equals the carrying amount of the bond times the market interest rate; amortization amounts vary period to period.
– Duration: a measure of a bond’s sensitivity to interest-rate changes; amortization generally lowers duration because principal is returned earlier.
Why amortization matters (practical impacts)
– Credit/default risk: Because principal is repaid over time, less principal is outstanding later in the life of the bond, which reduces lender/investor exposure to default risk compared with a bullet (single-maturity) bond.
– Interest-rate risk: Amortization reduces weighted-average maturity of cash flows, lowering duration and making the investment less sensitive to interest-rate moves.
– Accounting/tax effects: Issuers often amortize discounts or premiums into interest expense. How they amortize affects reported interest expense and taxable income.
How to build a basic amortization schedule (step-by-step)
1. Identify inputs:
– Principal (PV), annual nominal interest rate, payment frequency per year, and total term (years).
2. Convert the annual rate to the period rate: r = annual rate / payments per year.
3. Compute number of payments: n = years × payments per year.
4. Compute the fixed payment per period using the annuity formula:
– Payment = r × PV / [1 − (1 + r)^−n]
(This yields the constant periodic payment that fully amortizes the loan.)
5. For each period:
– Interest portion = outstanding balance × r.
– Principal portion = Payment − Interest portion.
– New balance = outstanding balance − Principal portion.
6. Repeat until balance is zero (last payment may be adjusted for rounding).
Worked numeric