+ i名(1+7%/2)7(1+9%/2)2(1+10%/2)2(1+11%/2)2(1+8%/2) + i名(1+7%/2)6(1+9%/2)(1+10%/2)2(1+11%/2)2(1+8%/2) + i名(1+7%/2)5(1+10%/2)2(1+11%/2)2(1+8%/2) + i名(1+7%/2)4(1+10%/2)(1+11%/2)2(1+8%/2) + i名(1+7%/2)3(1+11%/2)2(1+8%/2) + i名(1+7%/2)2(1+11%/2)(1+8%/2) + i名(1+7%/2)(1+8%/2)
+1] /(1+7%/2)10(1+5%/2)(1+7%/2)2(1+9%/2)2(1+10%/2)2(1+11%/2)2(1+8%/2)
= [i名×2.03467+ i名×1.89938+ i名×1.77309+ i名×1.63936+ i名×1.51572+ i名×1.39473 + i名×1.28339+ i名×1.17535+ i名×1.0764+ i名+1]/2.15853
2.15853= i名×14.79209＋1
半年的名义利息率：i名=(2.15853－1)÷14.79209=7.8321% 折算为全年的名义利息率：i名= (1+7.8321%)2-1=16.278%
42． 假设预测10年内的年通货膨胀率如下表： 年 份 通货膨胀率 1 -5% 2 -3% 3 -1% 4 5 6 6% 7 7% 8 8% 9 10% 10 10% 0% 4% 试确定票面利息率为8%的，一次还本付息的，10年期无风险债券的实际收益率。 解：
年平均通货膨胀率?10(1?5%)(1?3%)(1?1%)(1?0)(1?4%)(1?6%)(1?7%)(1?8%)(1?10%)(1?10%)?1
?101.40625?1?3.46805%无风险债券的实际收益率=(1+8%)/(1+3.46805%)-1=4.38%
43． 如果“习题42”中所述债券为每年付息，到期一次还本，其余假设条件不变，
请计算该债券的实际收益率。
解：
1=8%/(1+i)(1-5%)
+8%/(1+i)2(1-5%)(1-3%)
+8%/(1+i)3(1-5%)(1-3%)(1-1%)
+8%/(1+i)4(1-5%)(1-3%)(1-1%)(1+0)
+8%/(1+i)5(1-5%)(1-3%)(1-1%)(1+0)(1+4%)
+8%/(1+i)6(1-5%)(1-3%)(1-1%)(1+0)(1+4%)(1+6%)
+8%/(1+i)7(1-5%)(1-3%)(1-1%)(1+0)(1+4%)(1+6%)(1+7%)
+8%/(1+i)8(1-5%)(1-3%)(1-1%)(1+0)(1+4%)(1+6%)(1+7%)(1+8%)
+8%/(1+i)9(1-5%)(1-3%)(1-1%)(1+0)(1+4%)(1+6%)(1+7%)(1+8%)(1+10%)
+8%/(1+i)10(1-5%)(1-3%)(1-1%)(1+0)(1+4%)(1+6%)(1+7%)(1+8%)(1+10%)(1+10%) +1/(1+i)10(1-5%)(1-3%)(1-1%)(1+0)(1+4%)(1+6%)(1+7%)(1+8%)(1+10%)(1+10%) =8%/(1+i)0.95+8%/(1+i)20.9215+8%/(1+i)30.92129+8%/(1+i)40.92129+8%/(1+i)50.94878
+8%/(1+i)61.0057+8%/(1+i)71.0761+8%/(1+i)81.16219+8%/(1+i)91.27841+8%/(1+i)101.40625 +1/(1+i)101.40625 当i =5%时，有：
0.0802+0.07874+0.07501+0.07144+0.06607+0.05936+0.05283+0.04659+0.04034+0.03492
+0.43656=1.04206>1
当i =6%时，有：
0.07944+0.07727+0.07291+0.06878+0.063+0.05608+0.04944+0.04319+0.03704+0.03177+0.39708=0.97599<1
i实=5%＋[(1.04206-1)/(1.04206-0.97599)]×1%=5.6366%
44． 某人希望通过贷款100万元对房地产进行投资，房产的使用寿命为50年，房
产出租的名义收益率为10%。他预测10年内的年通货膨胀率如下表： 年 份 通货膨胀率 1 -6% 2 -4% 3 -2% 4 5 6 6% 7 8% 8 10% 9 11% 10 12% 0% 4% 贷款条件如下：贷款期限10年，贷款利息率为12%，每两年偿还20%的本金，每3个月按贷款余额支付一次利息。 试问该投资是否可行？
解：
第10年末的房产价值
=100(1-6%)(1-4%)(1-2%)(1+4%)(1+6%)(1+8%)(1+10%)(1+11%)(1+12%)×(50-10)/50 =115.19（万元）
第10年末的房产价值折算为现值
=115.19/(1-6%)(1-4%)(1-2%)(1+4%)(1+6%)(1+8%)(1+10%)(1+11%)(1+12%) =115.19/1.43987 =80（万元）
出租10年的实际收益现值 =10/(1-6%)
+10/(1-6%)(1-4%)
+10/(1-6%)(1-4%)(1-2%) +10/(1-6%)(1-4%)(1-2%)
+10/(1-6%)(1-4%)(1-2%)(1+4%)
+10/(1-6%)(1-4%)(1-2%)(1+4%)(1+6%)
+10/(1-6%)(1-4%)(1-2%)(1+4%)(1+6%)(1+8%)
+10/(1-6%)(1-4%)(1-2%)(1+4%)(1+6%)(1+8%)(1+10%)
+10/(1-6%)(1-4%)(1-2%)(1+4%)(1+6%)(1+8%)(1+10%)(1+11%)
+10/(1-6%)(1-4%)(1-2%)(1+4%)(1+6%)(1+8%)(1+10%)(1+11%)(1+12%) =10/0.94+10/0.9024+10/0.88435+10/0.88435+10/0.91973+10/0.97491 +10/1.0529+10/1.15819+10/1.28559+10/1.43987
=10.64+11.08+11.31+11.31+10.87+10.26+9.5+8.63+7.78+6.95 =98.33（万元）
年实际贷款利息率=(1+12%/4)4-1=12.55% 年实际贷款利息=100×12.55%=12.55（万元） 贷款实际利息支出现值 =12.55/(1-6%)
+12.55/(1-6%)(1-4%)
+10.04/(1-6%)(1-4%)(1-2%) +10.04/(1-6%)(1-4%)(1-2%)
+7.53/(1-6%)(1-4%)(1-2%)(1+4%)
+7.53/(1-6%)(1-4%)(1-2%)(1+4%)(1+6%)
+5.02/(1-6%)(1-4%)(1-2%)(1+4%)(1+6%)(1+8%)
+5.02/(1-6%)(1-4%)(1-2%)(1+4%)(1+6%)(1+8%)(1+10%)
+2.51/(1-6%)(1-4%)(1-2%)(1+4%)(1+6%)(1+8%)(1+10%)(1+11%)
+2.51/(1-6%)(1-4%)(1-2%)(1+4%)(1+6%)(1+8%)(1+10%)(1+11%)(1+12%)
=12.55/0.94+12.55/0.9024+10.04/0.88435+10.04/0.88435+7.53/0.91973+7.53/0.97491 +5.02/1.0529+5.02/1.15819+2.51/1.28559+2.51/1.43987 =13.35+13.91+11.35+11.35+8.19+7.72+4.77+4.33+1.95+1.74 =78.66（万元）
各年偿还的本金折算为现值 =20/(1-6%)(1-4%)
+20/(1-6%)(1-4%)(1-2%)
+20/(1-6%)(1-4%)(1-2%)(1+4%)(1+6%)
+20/(1-6%)(1-4%)(1-2%)(1+4%)(1+6%)(1+8%)(1+10%)
+20/(1-6%)(1-4%)(1-2%)(1+4%)(1+6%)(1+8%)(1+10%)(1+11%)(1+12%) =20/0.9024+20/0.88435+20/0.97491+20/1.15819+20/1.43987 =22.16+22.62+20.51+17.27+13.89 =96.45（万元）
投资该项目的净现值=（第10年末的房产价值折算为现值+出租10年的实际收益现值）
-（贷款利息支出现值+各年偿还的本金折算为现值）
=（80+98.33）-（78.66+96.45）=178.33－175.11 =3.22（万元） 投资该项目可取。