Nominal, Current, YTM & YTC — Q&A

The coupon is the fixed annual interest the issuer pays based on par. Yield is the bond’s overall rate of return, which incorporates purchase price and time — they differ when a bond trades at a discount or premium.

4%. Nominal yield = Annual income ÷ Par = $40 ÷ $1,000. It equals the stated coupon and never changes; market price is not part of the calculation.

5%. CY = Annual income ÷ Market price = $40 ÷ $800. For discount bonds, current yield is always higher than the coupon.

3.6%. CY = $40 ÷ $1,100. For premium bonds, current yield is always lower than the coupon.

It does not account for time — a 1-year and 30-year discount bond could show the same current yield even though the discount is earned over very different periods.

6.7%. YTM = [40 + ((1,000 − 800) ÷ 10)] ÷ ((1,000 + 800) ÷ 2) = (40 + 20) ÷ 900 = 6.7%.

2.9%. YTM = [40 − ((1,100 − 1,000) ÷ 10)] ÷ ((1,000 + 1,100) ÷ 2) = (40 − 10) ÷ 1,050 = 2.9%. Premium loss is subtracted over time.

YTM is 7% while the coupon is 5%. Higher YTM than coupon means the bond trades at a discount. “Basis” is another term for yield to maturity.

8.9%. YTC = [40 + ((1,000 − 800) ÷ 5)] ÷ ((1,000 + 800) ÷ 2) = (40 + 40) ÷ 900 = 8.9%. YTC exceeds YTM because the $200 discount is earned in half the time.

1.9%. YTC = [40 − ((1,100 − 1,000) ÷ 5)] ÷ ((1,000 + 1,100) ÷ 2) = (40 − 20) ÷ 1,050 = 1.9%. YTC is lower than YTM because the $100 premium loss is accelerated.