Final answer:
To calculate the full price of the bond, we need to calculate the present value of the future cash flows. In this case, the bond has a 6.5% coupon rate and a yield to maturity of 5.3%. The clean price of the bond can be calculated by adjusting the full price for the accrued interest.
Step-by-step explanation:
To calculate the full price of the bond, we need to calculate the present value of the future cash flows. In this case, the bond has a 6.5% coupon rate, which means it pays $65 in interest annually. The bond matures in just over 28 years, so we need to calculate the present value of the $65 coupon payments for 28 years, as well as the present value of the $1,000 face value payment at maturity. The yield to maturity is 5.3%, which we can use to discount the future cash flows. Therefore, the full price of the bond can be calculated as follows:
Full Price = (PV of Coupon Payments) + (PV of Face Value)
To calculate the clean price, we need to adjust the full price for the accrued interest. The bond was purchased 46 days after the most recent coupon payment, so we need to calculate the accrued interest for those 46 days. This can be calculated as:
Accrued Interest = (Coupon Payment / Coupon Period) * Accrual Days
Finally, the clean price can be calculated as:
Clean Price = Full Price - Accrued Interest