答案是用N年的和N-1年的数据算的，不用代入N-1年之前的利率数据。
比如说第三年的连续复利远期利率，S*e^13.0%*2*e^r3=S*e^{13.7%*3
r3=13.7%*3-13.0%*2=15.1%
r4=14.2%*4-13.7%*3=15.7%
r5=14.5%*5-14.2%*4=15.7%
算第三年的，可以先用13%的利率算2年，再考虑第三年的利率收益情况，所以不需要用第一年的数据。
你如果分每年算的话，第二年的数据应该代用你刚刚算出来第二年连续复利的14%，这样同样能算出15.1%。
r3=13.7%*3-12%-14%=15.1%}
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第二个算的不对，应该是S*e 13%*2*e r*1=S*e 13.7%*3 ，计算出r为第三年的远期利率，远期利率应该是理论值，你把它和实际的弄混了：）