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.

Keep the complete payment count explicit

Use the number of complete remaining coupon periods and retain the selected payment frequency beside nominal and effective annual yield. When checking another worksheet, match the price, redemption value, and payment count before comparing yields. This complete-period model does not reconstruct settlement between coupons or account for every date, accrued-interest, fee, or credit convention in a market quotation.

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.

The Complete-Period Bond Yield Calculator presents the same complete-period model with additional outputs, the Bond Price Calculator solves from yield to price, and the Time Value of Money Calculator isolates the lump-sum present-value core behind the bond equation.

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.