The current price of an annual coupon bond is 100. The yield to maturity is an annual effective rate of 8%. The derivative of the price of the bond with respect to the yield to maturity is -700.

Using the bond’s yield rate, calculate the Macaulay duration of the bond in years.

• 7.00
• 7.49
• 7.56
• 7.69
• 8.00

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: C.

Duration is the negative derivative of the price multiplied by one plus the interest rate and divided by the price. Hence, the duration is –(–700)(1.08)/100 = 7.56.

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.