A pension fund manager anticipates the purchase of a 20-year, 8 percent coupon Treasury bond at the end of two years. Interest rates are assumed to change only once every year at year-end, with an equal probability of a 1 percent increase or a 1 percent decrease. The Treasury bond, when purchased in two years, will pay interest semiannually. Currently, the Treasury bond is selling at par.

c. What prices are possible on the 20-year T-bonds at the end of year 1 and year 2?

This is the answer:

Currently, the bond is priced at par, $1,000 per $1,000 face value. At the end of the first year, either of two interest rates will occur.

(a) Interest rates will increase 1 percent to 9 percent (50 percent probability of either occurrence). The 20-year 8 percent coupon Treasury bond's price will fall to $907.9921 per $1,000 face value.

(b) Interest rates will decrease 1 percent to 7 percent (50 percent probability of occurrence). The 20-year 8 percent coupon Treasury bond's price will increase to $1,106.7754 per $1,000 face value.

Im just asking to show the work of how the answers $907.9921 and $1,106.7754 were achieved, thank you.