Complete-Period Bond Yield Calculator

Enter the bond’s present-value price, face value, annual coupon rate, payment frequency, and a positive whole number of complete coupon periods remaining. The result is a periodic cash-flow yield expressed as both a nominal annual rate and an effective annual rate.

Inputs and method

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

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

The periodic yield r is the rate that satisfies:

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

A result is accepted only when the modeled price differs from the entered price by no more than 10^-8. The annual rates are:

$\text{nominal annual yield}=rm\times100\%$

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

Current yield is annual coupon income divided by entered price. It does not include the redemption gain or premium. The other results show annual coupon income, the complete payment count, total coupons before maturity, and the difference between price and face value.

Worked example

For a $1,350 price, $1,500 face value, 6% annual coupon, annual frequency, and 15 complete periods, nominal and effective annual yield both display as 7.11%. Current yield is 6.67%, annual coupon income is $90.00, coupons before maturity total $1,350.00, and the redemption gain is $150.00.

Assumptions and limitations

This educational model assumes settlement immediately after a coupon payment, equal complete periods, no accrued interest, and entered price equal to the present value of the modeled cash flows. It has no dates, stub periods, day-count convention, or clean-to-dirty price conversion.

It is not a conventional dated market YTM quote. It does not model default, calls, taxes, liquidity, transaction costs, changing cash flows, or coupon reinvestment. Negative yields are accepted when positive modeled cash flows and the entered price imply one.

Sources

• FINRA, Bond Yield and Return — explains current yield, yield to maturity, and bond return drivers; it does not validate this calculator’s settlement assumptions.
• SEC, Investor Bulletin: Corporate Bonds — provides corporate-bond pricing, yield, and risk context; it does not define this complete-period model.
• FINRA, Bonds — provides general bond and risk context; it does not validate a dated market-convention yield here.
• U.S. TreasuryDirect, Treasury Bonds — describes Treasury coupon payments and maturity; it does not establish conventions for other securities.
• OpenStax, Rice University, Principles of Finance, 2022 first edition — supports present value of coupon and principal cash flows and nominal/effective yield concepts; it does not select settlement, accrued-interest, day-count, or stub conventions.
• 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 coupon periods.