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Government Bond Price Formula:
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The government bond price formula calculates the present value of a bond by discounting its future cash flows (par value at maturity and coupon payments) using the yield to maturity. This helps investors determine the fair value of a bond in the market.
The calculator uses the bond pricing formula:
Where:
Explanation: The formula discounts the bond's par value back to present value and adds the present value of all coupon payments to determine the bond's fair price.
Details: Accurate bond pricing is essential for investors to make informed decisions, assess bond attractiveness compared to other investments, and understand the relationship between bond prices and interest rates.
Tips: Enter par value in USD, yield as a decimal (e.g., 0.05 for 5%), years to maturity, and present value of coupons in USD. All values must be positive numbers.
Q1: Why does bond price change with yield?
A: Bond prices and yields have an inverse relationship. When yields rise, existing bond prices fall to make them competitive with new bonds offering higher yields.
Q2: What is the difference between yield and coupon rate?
A: Coupon rate is the fixed interest rate the bond pays, while yield reflects the total return considering current price and remaining payments.
Q3: How do I calculate the present value of coupons?
A: The present value of coupons can be calculated using the formula for the present value of an annuity, or you can use a separate coupon calculator.
Q4: Why do longer-term bonds have more price volatility?
A: Longer-term bonds have more duration risk because their cash flows are discounted over a longer period, making them more sensitive to interest rate changes.
Q5: Are government bonds always risk-free?
A: While generally considered low-risk, government bonds still carry interest rate risk, inflation risk, and in some cases, sovereign default risk.