Original questions: We expect the yields of maturity to increase by 1% from their present level. We have a 25 year 8% paying bond with a required rate of 7%. We want to switch to a 4 year 8% bond with a market rate of 6%. What shall we gain if we act on our expectation, and it transpires. If rates instead increase, what will be the result? Solution provided : Pv of bond = C x 1-(1+r)-n /r + FV/ (1+r)n Value of 25 year bond when YTM is 7% PV = C x 1-(1+r)-n/ r + FV / (1+r)n = 8 X 1-(1+0.07)-25 + 100/(1+0.07)25 = 111.65 Value of 25 year bond when YTM increased to 8% PV = C x 1-(1+r)-n/ r + FV / (1+r)n = 8 X 1-(1+0.08)-25 + 100/(1+0.08)25 = 100 Value of 4 year bond which YTM is 6% PV = C x 1-(1+r)-n/ r + FV / (1+r)n = 8 X 1-(1+0.06)-4 + 100/(1+0.06)4 = 106.93 Please please explain step by step how we got to 111.65, 100 and 106.93. I tried to follow the calculations and could not match it. Thank you