When a bond is issued above or below its face value, the stated coupon rate differs from the market yield embedded in the issue price. Under IFRS 9 and ASC 320, the effective interest method amortizes the premium or discount using the rate that equates the issue price to the present value of future cash flows. This calculator solves for that effective interest rate.
How to use this calculator
- Enter the bond's face (par) value and the actual issue price.
- Input the stated annual coupon rate and the number of years to maturity.
- Set coupon payments per year (1 = annual, 2 = semi-annual, 12 = monthly).
- Review the effective annual rate, periodic rate, and premium/discount classification.
- Use the EIR in the Bond Amortization Schedule calculator to build period-by-period entries.
Formula
The effective interest rate is the discount rate that sets the present value of all future coupon payments plus face value equal to the issue price: Issue price = Σ [Coupon / (1 + r)^t] + Face / (1 + r)^n. The effective annual rate = (1 + periodic rate)^paymentsPerYear − 1. A discount (issue price < face) produces an EIR above the coupon rate; a premium produces an EIR below the coupon.
Example
A $1,000,000 face bond issued at $950,000 with a 5% coupon, 10-year term, and semi-annual payments has an effective annual rate above 5% — the investor earns more than the stated coupon because they paid less than par.
Frequently asked questions
Why is the effective rate higher than the coupon on a discount bond?
The investor paid less than face value but receives the full face amount at maturity plus coupon payments. The extra return is embedded in the discount, raising the yield above the stated coupon.
Is this the same as yield to maturity (YTM)?
For a bond held to maturity with no call features, the effective interest rate at issuance equals the yield to maturity. This calculator assumes fixed cash flows with no early redemption.
How is the EIR used in accounting?
Each period, interest expense = carrying value × periodic EIR. The difference between interest expense and the cash coupon amortizes the premium or discount into the carrying amount.
What if the bond pays monthly coupons?
Set payments per year to 12. The solver finds the monthly periodic rate and annualizes it compounding over 12 periods.