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What This Calculator Does
This calculator calculates the total nominal return and annualized rate of return (CAGR) for a Treasury Bond, accounting for coupon income and capital gains from discount purchases.
How to Use This Calculator
Enter your purchase price, face value, coupon rate, years held, and final selling price (typically face value if held to maturity). Click Calculate to find your total and annualized returns.
How the Calculation Works
The underlying math engine processes your inputs using exact formulas. This systematic approach ensures professional, institutional-grade calculation precision:
Mathematical Formula
Formula Legend:
- · Accumulated Coupon Income = Face Value * (Coupon Rate / 100) * Years.
- · Annualized Return % = [((Total Return + Purchase Price) / Purchase Price) ^ (1 / Years) - 1] * 100.
Practical Example
An investor buys a US Treasury Bond at a discount price of $9,500. The bond has a $10,000 face value and a 4.0% annual coupon. They hold the bond for 5 years and sell it at maturity for $10,000:
Step-by-Step Mathematical Walkthrough:
- 1 Purchase Price = $9,500; Selling Price = $10,000.
- 2 Total Coupon Income over 5 years = $10,000 * 0.04 * 5 = $2,000.
- 3 Capital Gain = $10,000 - $9,500 = $500.
- 4 Total Return Amount = $2,000 + $500 = $2,500.
- 5 Annualized Return (CAGR) = [($12,000 / $9,500)^(1/5) - 1] * 100 = 4.79%.
Important Assumptions & Notes
- The bond pays coupons annually for standard holding calculation models.
- The selling price represents full realized value upon disposal.
- Inflation or taxes are not subtracted from returns.
Common Mistakes or Considerations
- Failing to account for the difference between purchase price and par value, which represents a key source of return for discount bonds.
- Using yield to maturity (YTM) for short-term holding periods. If you sell before maturity, your return depends on the prevailing market price at that time.
Frequently Asked Questions
What is a US Treasury Bond?
A debt security issued by the US Department of the Treasury to fund government spending. They are considered exceptionally safe because they are backed by the US government.
Are US Treasury Bond returns taxed?
Treasury interest is subject to federal income tax, but it is exempt from all state and local income taxes, which increases your net return.
What happens if I sell a Treasury bond before maturity?
You can sell it on the secondary market. If interest rates have risen since you bought it, you may have to sell it at a loss. If rates have fallen, you may sell it at a premium.