dopecalc

Bond Calculator

Calculate the present value of a bond's future cash flows, current yield, and yield to maturity given the face value, coupon rate, and market interest rate.

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About this Calculator

Calculate the present value of a bond's future cash flows, current yield, and yield to maturity given the face value, coupon rate, and market interest rate.

Formula & Calculations

Formula

Bond Price = C × [1 - (1+r)^-n] / r + FV / (1+r)^n; Current Yield = Annual Coupon / Bond Price; YTM = Market Rate (at fair pricing)
Where:
  • FV=Face value (par value) of the bond
  • C=Annual coupon payment = Face Value × Coupon Rate
  • n=Years to maturity
  • r=Current market interest rate (discount rate)
  • PV=Present value (bond price)
  • CY=Current yield = Annual Coupon / Bond Price × 100

Assumptions

  • Annual coupon payments are assumed (not semi-annual, for simplicity).
  • The bond's yield to maturity is approximated by the current market rate.
  • Bond prices move inversely to interest rates: when market rates rise, bond prices fall.
  • All cash flows are discounted at the current market rate.

Calculation Examples

Example 1

Inputs:Face Value: $1,000, Coupon: 5%, Years: 10, Market Rate: 6%
Result:Bond Price: $926.40, Current Yield: 5.40%, YTM: 6.00%

When the market rate (6%) exceeds the coupon rate (5%), the bond sells at a discount ($926.40) so its current yield matches the market.

Example 2

Inputs:Face Value: $1,000, Coupon: 7%, Years: 5, Market Rate: 4%
Result:Bond Price: $1,133.60, Current Yield: 6.18%, YTM: 4.00%

When the coupon rate exceeds the market rate, the bond sells at a premium above face value. The current yield reflects the premium price.

Example 3

Inputs:Face Value: $5,000, Coupon: 3%, Years: 15, Market Rate: 3%
Result:Bond Price: $5,000, Current Yield: 3.00%, YTM: 3.00%

When the coupon rate equals the market rate, the bond trades at par (face value). The current yield equals both the coupon rate and YTM.

Frequently Asked Questions

Why do bond prices go down when interest rates go up?

Bonds pay a fixed coupon. When market interest rates rise, newly issued bonds offer higher coupon payments, making existing bonds with lower coupons less attractive. To compensate, the price of existing bonds falls so their current yield matches the new market rate.

What is the difference between current yield and yield to maturity?

Current yield is the annual coupon payment divided by the bond's current price. Yield to maturity (YTM) is the total return expected if the bond is held to maturity, accounting for both coupon payments and any gain or loss from the difference between the purchase price and face value at maturity.