仍然设利率特征值k为100r,ƒ为终值系数,p为现值系数,速算系数为q,那么有:1.已知利率特征值k,求10年后的终值系数ƒ。规则:q+0.1k=5.2,q=5.2-0.1k,ƒ=k/q例如:k=17时,q=5.2-0.1×17=3.5,ƒ=k/q=17/3.5=4.86;k=25时,q=5.2-0.1×25=2.7,ƒ=k/q=25/2.7=9.3。对于10≦k≦45时的所有终值系数的估算值、实际值和误差参见下表2。表2 积累期限为10年的复利终值系数的实际值与估计值k101112131415161718192021实际值2.592.843.113.403.714.054.414.815.235.706.196.73估计值[ii]2.382.683.003.333.684.054.444.865.295.766.256.77误差%[iii]-8-6-4-2-10111111k222324252627282930313233实际值7.317.938.599.3110.0910.9211.8112.7613.7914.8816.0617.32估计值7.337.938.579.2610.0010.8011.6712.6113.6414.7616.0017.37误差%000-1-1-1-1-1-1-100k343536373839404142434445实际值18.6720.1121.6523.2925.0526.9228.9331.0633.3335.7638.3341.08估计值18.8920.5922.5024.6727.1430.0033.3337.2742.0047.7855.0064.29误差%12468111520263443562.已知10年后的终值系数ƒ,求利率特征值k规则:∵ƒ=k/q=k/(5.2-0.1k),∴k=5.2ƒ/(1+0.1ƒ)=5.2/(1/ƒ+0.1)=5.2/(p+0.1)例:ƒ=8时,k=5.2/(1/ƒ+0.1)=5.2/(1/ 8+0.1)=5.2/0.225=23.1;ƒ=9时,k=5.2/(1/ 9+0.1)=5.2/0.211=24.6。3.已知利率特征值k,求10年初的现值系数p规则:p=1/ ƒ=q/k=(5.2-0.1k)/k例:k=18时,q=5.2-0.1k=5.2-1.8=3.4,p=3.4/18=0.19