How to use the bond premium and discount amortization calculator
- Enter the face value, the coupon rate, the years to maturity and how many coupons per year are paid.
- Choose whether you know the market yield or the price paid, then enter that figure.
- Read the price, the coupon each period and the total interest expense, then check the schedule.
- Download the CSV for every period, with opening value, interest, coupon, amortization and closing value.
Formula
price = sum of coupon / (1 + y)^k for k = 1 to n, plus face / (1 + y)^n
interest = opening carrying value x y
amortization = interest - coupon
closing value = opening value + amortization
The periodic yield y is the yearly yield divided by the coupons per year. When you enter the price, the page finds y by bisection. Each period is rounded to the cent, and the last period clears the leftover cents so the carrying value ends at the face value.
A 5 year bond bought at a discount
Face value is $100,000, the coupon is 5% paid twice a year ($2,500), and the market yield is 6%, so y is 3% per period over 10 periods. The price is $95,734.90, a discount of $4,265.10.
In period 1 the interest is $95,734.90 x 3% = $2,872.05. The coupon is $2,500, so $372.05 of discount is amortized and the carrying value rises to $96,106.95. Total interest over the term is $29,265.10, which is the $25,000 of coupons plus the $4,265.10 discount. A 7% coupon at the same yield is priced at a premium of $4,265.10, and total interest is $30,734.90.
Premium versus discount
When the coupon is lower than the market yield, the bond sells below its face value, and the discount is earned back as extra interest. When the coupon is higher, the bond sells above face value, and the premium reduces the interest recognized each period. Either way the carrying value moves steadily toward the face value and reaches it on the maturity date.
Effective interest versus straight line
The effective interest method applies a constant yield to a changing carrying value, so the amortization grows for a discount bond and shrinks for a premium bond. The straight-line figure shown in the results spreads the premium or discount evenly. Accounting rules and tax rules differ in which is allowed, so confirm with your accountant. For yields and sensitivity, use the Bond Yield Calculator and the Bond Duration and Convexity Calculator.
Assumptions and limits
- Coupons are paid at the end of each period, and the purchase date is a coupon date, so no accrued interest is modeled.
- The yearly yield is split evenly across periods, and the bond is held to maturity.
- Amounts are rounded to the cent each period. The final period adjusts so the carrying value equals the face value.
- Fees, taxes and call features are not modeled. The treatment for accounting or tax may differ.
Frequently asked questions
What does carrying value mean?
It is the amount the bond is recorded at on your books after the premium or discount has been partly amortized. It starts at the price paid and ends at the face value.
Why does amortization change each period?
Interest is the carrying value times the yield, and the carrying value changes every period. As it moves toward face value, interest and amortization move with it.
Can I enter the price instead of the yield?
Yes. Choose Price paid and the page finds the yield that makes the bond worth that price. If no yield between negative 50% and 1,000% per period fits, it asks you to check the price.
What if the price equals the face value?
Then the bond is at par, the coupon equals the interest each period, and the amortization is zero. The schedule still shows each period so you can confirm that.