Which of the following describes the basis for Yield to Maturity calculation?

• A. Annual Interest +/- (Discount(Premium)/years to maturity)/Average Price of the Bond
• B. Annual Interest +/- (Discount(Premium))/years to maturity
• C. Annual Interest +/- (Discount)/years to maturity/Par
• D. Annual Interest +/- (Par/Premium)/years to maturity

Answer: (A)

Yield to maturity uses a simple, intuitive way to estimate your total annual return if you hold the bond to its maturity. You start with the annual coupon income, then adjust for the fact you’ll recover (or lose) the difference between par value and the purchase price over the years to maturity. That adjustment is the annual amortization, calculated as the discount or premium (the amount par minus price, positive if it’s a discount, negative if it’s a premium) divided by the number of years to maturity. Put those together and then place them over the bond’s current price context by dividing by the average price of the bond, typically approximated as (Par + Price)/2.

For example, if par is 100, price is 95, annual coupon is 6, and there are 5 years to maturity, the annual amortization is (100 − 95)/5 = 1. So the numerator is 6 + 1 = 7. The average price is (100 + 95)/2 = 97.5, giving an approximate yield of 7 / 97.5 ≈ 7.18%.

That’s why the correct basis includes the annual coupon plus the annual amortization of the discount or premium, all divided by the average price. Other formulations omit the average price or mix the terms in a way that doesn’t reflect how YTM is approximated.