Bond X is a premium bond making annual payments. The bond pays an 8 percent coupon, has a YTM of 6 percent, and has 13 years to maturity. Bond Y is a discount bond making annual payments. This bond pays a 6 percent coupon, has a YTM of 8 percent, and also has 13 years to maturity. If interest rates remain unchanged, you would expect that one year from now, Bonds X and Y will be priced at ? and ?, respectively. In three years, they will be priced at ? and ? . In eight years: ? and ? . In 12 years: ? and ?. And in 13 years: ? and ? . (

To determine the prices of Bond X and Bond Y at different time points, we will need to use the formulas for calculating bond prices.

The formula for calculating the price of a bond is:

Price = (Coupon Payment / (1 + YTM)^t) + (Coupon Payment / (1 + YTM)^(t+1)) + ... + (Coupon Payment + Face Value / (1 + YTM)^(t+n))

Where:
- Coupon Payment is the annual coupon payment of the bond
- YTM is the Yield to Maturity (expressed as a decimal)
- t is the time period (in years)
- n is the number of years to maturity

Let's substitute the provided information into the formula to calculate the prices of Bonds X and Y at different time points:

One year from now (t = 1):
Bond X:
Price_X(1) = (Coupon Payment_X / (1 + YTM_X)^1) + (Face Value_X / (1 + YTM_X)^14)
= (0.08 * Face Value_X / (1 + 0.06)^1) + (Face Value_X / (1 + 0.06)^14)

Bond Y:
Price_Y(1) = (Coupon Payment_Y / (1 + YTM_Y)^1) + (Face Value_Y / (1 + YTM_Y)^14)
= (0.06 * Face Value_Y / (1 + 0.08)^1) + (Face Value_Y / (1 + 0.08)^14)

Three years from now (t = 3):
Bond X:
Price_X(3) = (Coupon Payment_X / (1 + YTM_X)^3) + (Coupon Payment_X / (1 + YTM_X)^4) + (Coupon Payment_X / (1 + YTM_X)^5) + (Face Value_X / (1 + YTM_X)^16)
= (0.08 * Face Value_X / (1 + 0.06)^3) + (0.08 * Face Value_X / (1 + 0.06)^4) + (0.08 * Face Value_X / (1 + 0.06)^5) + (Face Value_X / (1 + 0.06)^16)

Bond Y:
Price_Y(3) = (Coupon Payment_Y / (1 + YTM_Y)^3) + (Coupon Payment_Y / (1 + YTM_Y)^4) + (Coupon Payment_Y / (1 + YTM_Y)^5) + (Face Value_Y / (1 + YTM_Y)^16)
= (0.06 * Face Value_Y / (1 + 0.08)^3) + (0.06 * Face Value_Y / (1 + 0.08)^4) + (0.06 * Face Value_Y / (1 + 0.08)^5) + (Face Value_Y / (1 + 0.08)^16)

Eight years from now (t = 8):
Bond X:
Price_X(8) = Summation of each Coupon Payment and Face Value discounted by (1 + YTM_X)^(t+13)

Bond Y:
Price_Y(8) = Summation of each Coupon Payment and Face Value discounted by (1 + YTM_Y)^(t+13)

Twelve years from now (t = 12):
Bond X:
Price_X(12) = Summation of each Coupon Payment and Face Value discounted by (1 + YTM_X)^(t+1)

Bond Y:
Price_Y(12) = Summation of each Coupon Payment and Face Value discounted by (1 + YTM_Y)^(t+1)

Thirteen years from now (t = 13):
Bond X:
Price_X(13) = Coupon Payment_X + Face Value_X

Bond Y:
Price_Y(13) = Coupon Payment_Y + Face Value_Y

By plugging in the given values (Coupon Payment, YTM, and Face Value), you should be able to calculate the prices of Bonds X and Y at each time point.