NO.PZ2018091705000045
问题如下：
Peter is 79 years old and his wife Lucy is 68 years old. They would like to maintain their living standards with spending requirement of $300,000 in real terms.
Assuming inflation rate is 2% and nominal risk-free rate is 4%. The survival probabilities for the next three years are listed in the following table:
Peter and Lucy’s core capital spending needs over the next three years are：
选项：
A. 860,490
B. 900,000
C. 824,659
解释：
A is correct.
考点：Estimating core capital with mortality tables
解析：每年存活的联合概率为：
第一年: P (joint survival) =0.9355+0.9831-0.9355×0.9831=0.9989
第二年：P (joint survival) =0.8702+0.9649-0.8702×0.9649=0.9954
第三年：P (joint survival) =0.8038+0.9457-0.8038×0.9457=0.9893
每年的必要支出为300,000，该数字是in real terms，而不是nominal，因此需要用real rate进行折现，real rate=nominal free risk rate- inflation rate=4%-2%=2%
第一年现值=(300,000×0.9989)/(1+2%)=293,794
第二年现值=(300,000×0.9954)/(1+2%)^2 =287,024
第三年现值=(300,000×0.9893)/(1+2%)^3 =279,672
因此core capital=293,794+287,024+279,672=860,490
老师您好，请问要如何用本题real spending和real risk free rate的方法计算基础班讲义上的例题呢？讲义上的inflation rate是2%，risk free rate是2%，计算时spending有乘以 1+inflation rate，但求PV时用的是 1+2%的折现率，基于分子和分母一致，可以得知例题给的risk free rate 2%是real而非nominal？如果用real的方法计算，real risk free rate = nominal risk free rate - inflation rate = 2% - 2% = 0，所以若用real的方式计算，分母的折现率应该用1+0%吗？这样算出来的结果和例题给的答案似乎不同，麻烦老师解惑，谢谢！