Complete-Period Bond Yield Worksheet

This worksheet solves a stylized fixed-rate bond present-value equation. Enter a positive whole number of complete coupon periods remaining. The model does not round years into periods.

Scope and assumptions

The equation assumes settlement immediately after a coupon payment, equal complete periods, no accrued interest, and entered price equal to the present-value price. It does not model settlement dates, stub periods, day-count rules, taxes, default, calls, or clean/dirty quote conversion.

For face value F, annual coupon rate q, coupon frequency m, and complete periods N, coupon per period is:

$C = \frac{Fq}{m}$

The worksheet solves periodic yield r from:

$P = \sum_{t=1}^{N}\frac{C}{(1+r)^t}+\frac{F}{(1+r)^N}$

It accepts a solution only when the absolute price residual is no greater than 10^-8. Annual outputs are:

$\text{nominal annual yield}=r m \times 100\%$

$\text{effective annual yield}=((1+r)^m-1)\times100\%$

For a $980 price, $1,000 face value, 5% annual coupon, annual frequency, and 10 complete periods, nominal and effective annual yield both display as 5.26%. Annual coupon income is $50.00, redemption gain is $20.00, and coupons before maturity total $500.00.

Interpretation

This educational complete-period result is not a dated market-convention YTM. Actual quoted yield can depend on accrued interest, settlement, coupon dates, day-count conventions, embedded options, taxes, liquidity, and credit risk.

Sources

• OpenStax, Rice University, Principles of Finance, 2022 first edition — supports present value of coupon and principal cash flows and nominal/effective yield concepts.
• U.S. TreasuryDirect, Understanding pricing and interest rates — supports the price/yield relationship and the need for security-specific terms; it does not support inventing a coupon period by rounding.