Bond Calculator

How to use this calculator

1. Enter or choose work out.
2. Enter or choose face (par) value.
3. Enter or choose coupon rate (per year).
4. Enter or choose years to maturity.
5. Enter or choose coupons per year.
6. The price updates as you type. Use Copy result or Share to keep it.

Method

Price = Σ C ÷ (1 + y/m)^t + F ÷ (1 + y/m)^n for t = 1…n; Current yield = Annual coupon ÷ Price; Macaulay D = Σ (t/m) × PV(CF_t) ÷ Price; Modified D = Macaulay D ÷ (1 + y/m)

C

coupon per period = F × coupon rate ÷ m

F

face value

y

yield to maturity

m

coupons per year

n

coupons remaining

Worked example

1. Coupon per half-year C = 1,000 × 8% ÷ 2 = 40; yield per period = 5%; n = 20.
2. Coupons: 40 × (1 − 1.05^−20) ÷ 0.05 = 498.49. Face value: 1,000 ÷ 1.05^20 = 376.89.
3. Price = 498.49 + 376.89 = 875.38; current yield = 80 ÷ 875.38 = 9.14%.

A 10-year 8% semi-annual bond priced to yield 10% is worth $875.38, a discount to its $1,000 face value.

What the result means

When the yield is above the coupon rate the bond trades below face value, and vice versa. Modified duration is the approximate percentage price change for a 1 percentage-point change in yield: a duration of 6.5 means roughly a 6.5% fall if yields rise by 1 point.

Assumptions and limits

• The bond is priced on a coupon date, so there is no accrued interest (clean and dirty prices are equal).
• All coupons and the face value are paid in full and on time.
• The yield is compounded at the coupon frequency, the usual bond-market convention.
• Call and put features, default risk and day-count conventions between coupon dates are not modelled.
• Yield to maturity assumes coupons are reinvested at the same yield.

Sources

• U.S. SEC Investor.gov