Yield to Maturity (YTM) Calculator

Result

YTM (annual nominal): 5.661689%

Repriced Value (from YTM): 950.0000

Macaulay Duration: 7.927278 years

Modified Duration: 7.709047 years

YTM is the single discount rate that equates the present value of coupon and principal payments with the current price.

Cash Flow Schedule

Period	Cash Flow	Discount Factor	Present Value	Cumulative PV
1	25.000000	1.028308	24.311772	24.311772
2	25.000000	1.057418	23.642489	47.954261
3	25.000000	1.087352	22.991632	70.945893
4	25.000000	1.118133	22.358692	93.304585
5	25.000000	1.149786	21.743177	115.047762
6	25.000000	1.182335	21.144606	136.192368
7	25.000000	1.215805	20.562513	156.754881
8	25.000000	1.250222	19.996445	176.751325
9	25.000000	1.285614	19.445960	196.197285
10	25.000000	1.322008	18.910629	215.107915
11	25.000000	1.359432	18.390036	233.497951
12	25.000000	1.397915	17.883774	251.381725
13	25.000000	1.437488	17.391449	268.773174
14	25.000000	1.478181	16.912678	285.685851
15	25.000000	1.520026	16.447086	302.132938
16	25.000000	1.563056	15.994312	318.127250
17	25.000000	1.607303	15.554002	333.681252
18	25.000000	1.652804	15.125814	348.807066
19	25.000000	1.699592	14.709414	363.516480
20	1,025.000000	1.747705	586.483517	949.999997

You can export the schedule to CSV or PDF using the buttons above.

Example Data

Sample bonds to demonstrate typical parameter combinations and resulting yields.

Face	Coupon %	Price	Years	Frequency	YTM %
1,000.00	5.0000	950.00	10.00	Semiannual	5.661689
1,000.00	3.0000	1,020.00	7.00	Annual	2.682814
1,000.00	8.0000	1,100.00	15.00	Quarterly	6.923053

Formula Used

The bond price is the present value of all future cash flows discounted at the yield to maturity:

Price = Σ[t=1..N] [ (C/f × Face) / (1 + y/f)^t ] + Face / (1 + y/f)^N
Where:
- y is the annual nominal YTM
- f is coupon frequency per year (1, 2, 4, or 12)
- C is annual coupon rate as a decimal
- N is total number of coupon periods (Years × f)

YTM is the rate y that solves the above equation for the observed Price. This tool uses a robust bisection root finder to compute y.

How to Use

Enter Face Value, Coupon Rate, Price, Years to Maturity, and select Coupon Frequency.
Click Calculate to compute the annual nominal YTM and key risk measures.
Review the Cash Flow Schedule and the PV by Period chart for insight.
Export the schedule using Download CSV or Download PDF.
Adjust inputs to compare bonds or test sensitivities.

FAQs

1) Does this YTM assume reinvestment of coupons?

YTM assumes interim coupons are reinvested at the same yield. Realized returns can differ if reinvestment rates vary.

2) What is the difference between Macaulay and Modified Duration?

Macaulay duration measures the weighted average time to cash flows. Modified duration adjusts for yield compounding and estimates price sensitivity to small yield changes.

3) Why might YTM be unavailable for some inputs?

Extreme prices or parameters can prevent a valid bracket for the root. Try changing price, years, or frequency to obtain a monotonic price–yield relationship within bounds.

4) Does this support day-count conventions or settlement dates?

For simplicity, the calculator uses whole periods based on frequency. Professional valuation may incorporate settlement dates and day-count conventions.

5) Is the yield nominal or effective?

The reported yield is an annual nominal rate consistent with the chosen coupon frequency. Effective annual yield equals (1 + y/f)^f − 1.