Final answer:
The Macaulay duration of a bond with a coupon of 6.2 percent, five years to maturity, and a current price of $1,064.70 can be calculated using the formula: Macaulay Duration = (C1 x T1 + ... + Cn x Tn) / V. To find the modified duration, divide the Macaulay duration by (1 + Y), where Y is the yield to maturity.
Step-by-step explanation:
The Macaulay duration of a bond can be calculated using the formula:
Macaulay Duration = ( C1 x T1 + … + Cn x Tn) / V
where C1, C2, ..., Cn are the cash flows at each period and T1, T2, ..., Tn are the time periods. V is the bond's current price.
For the given bond with a coupon of 6.2 percent and five years to maturity, let's assume an annual coupon payment of $62 (6.2% x $1,000), and a final payment of $1,062 (principal + final coupon payment). The bond's cash flows would be:
C1 = $62, C2 = $62, C3 = $62, C4 = $62, C5 = $1,062
T1 = 1, T2 = 2, T3 = 3, T4 = 4, T5 = 5
Substituting these values into the formula, we get:
Macaulay Duration = (($62 x 1) + ($62 x 2) + ($62 x 3) + ($62 x 4) + ($1,062 x 5)) / $1,064.70
Simplifying this calculation will give you the answer for the Macaulay duration. To find the modified duration, you will need to divide the Macaulay duration by (1 + Y), where Y is the yield to maturity, expressed as a decimal.
Remember to round your answers to 3 decimal places.