Question

A 6.2% coupon bond is trading with a full price of 78.88 . Assume the yield to maturity is 8.6%. Find the full price in 9 days assuming the yield to maturity does not change over the time horizon. Assume we are 46 days from the most recent coupon date and that there are 181 days in the coupon period. Use actuallactual day count convention. (Give you answer to 3 decimal places in this quesiton.)

Answer 1

The full price of the bond in 9 days is $98.723.

Step-by-step explanation:

To find the full price in 9 days, we need to calculate the present value of the bond using the yield to maturity. The bond's yield to maturity is 8.6%, and we are 46 days from the most recent coupon date. Since there are 181 days in the coupon period, the time remaining until the next coupon payment is 135 days (181 - 46). Using the actual/actual day count convention, the fraction of the coupon period remaining is 135/181. Now, we can calculate the full price in 9 days: Full Price = Coupon Payment / (1 + Yield to Maturity/2)^(2 * Days until next coupon payment / Coupon Period) + Face Value / (1 + Yield to Maturity/2)^(2 * Days until next coupon payment / Coupon Period) = $3.10 / (1 + 0.086/2)^(2 * 135/181) + $100 / (1 + 0.086/2)^(2 * 135/181) = $3.10 / (1.043)^0.746 + $100 / (1.043)^0.746 = $3.098 + $95.625 = $98.723.