I don't get it, where did the 85.780408 come from? what is the formula for that? also the price in 7 years, where did the number come from?

duration=7.0029 years 10 year bond with 8% coupon selling at 85.503075 per 100 parvalue, YTM=10.40% After the bond is purchased and before the first coupon is received, interest rates go up to 11.40% HPR for 10 years 8*1.11449+8*1.11418+8*1.114^7+8*1.11416+8*1.11445+8*1.114^4+8*1.114^3+8*1.114^2+8*1.114+8+100= 236.3801948 85.503075*(1+r)^10=236.38 r= 10.70% 85.780408 HPR for 4 years price in 4 years: 8*1.114^3+8*1.114^2+8*1.114+8+85.780408= 123.6801324 85.503075*(1+r)^4=123.68 r= 9.67% HPR for 7 years price in 7 years: 91.748833 8*1.11416+8*1.11415+8*1.114^4+8*1.11413+8*1.114^2+8*1.114+8+91.748833= 170.9840156 85.503075*(1+r)^7=170.9840 10.40% r=