老师，好像对于goal2是用的后付模式来算，是否也应该用先付模式？问题如下图：
NO.PZ201803130100000602 问题如下 Construtheoverall goals-baseasset allocation for the Armstrongs given their three goalsanAbbott’s suggestion for investing any excess capital. Show yourcalculations.Show your calculations. Guiline Answer:■ The mole thshoulselectefor eagois the one thoffers the highest return given the time horizon anrequireprobability of success.■ Approximately 16.4%, 12.7%, 50.4%, an20.5% shoulinvestein Moles an respectively. The appropriate goals-baseallocation for the Armstrongs is follows:Supporting calculations:For Go1, whiha time horizon of five years ana requireprobability of success of 85%, Mole C shoulchosen because its 4.4% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go1 is calculatefollows:N = 5, FV = –5,000,000, I/Y = 4.4%; CPT PV = $4,031,508 (or $4.03 million)So, approximately 50.4% of the totassets of $8 million (= $4.03 million/$8.00 million) shoulallocateto Mole For Go2, whiha time horizon of 10 years ana requireprobability of success of 99%, Mole B shoulchosen because its 2.2% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go2 is calculatefollows:PV=$100,000/(1.022)1+$100,000(1.03)1/(1.022)2+$100,000(1.03)2/(1.022)3+...+$100,000(1.03)9/(1.022)10PV = $1,013,670 (or $1.01 million)So, approximately 12.7% of the totassets of $8 million (= $1.01 million/$8.00 million) shoulallocateto Mole For Go3, whiha time horizon of 25 years ana requireprobability of success of 75%, Mole shoulchosen because its 7.5% expectereturn is higher ththe expectereturns of all the other moles. The present value ofGo3 is calculatefollows:N = 25, FV = –10,000,000, I/Y = 7.5%; CPT PV = $1,639,791 (or $1.64 million)So, approximately 20.5% of the totassets of $8 million (= $1.64 million/$8.00 million) shoulallocateto Mole Finally, the surplus of $1,315,032 (= $8,000,000 – $4,031,508 – $1,013,670 –$1,639,791), representing 16.4% (= $1.32 million/$8.00 million), shoulinvestein Mole A following Abbott’s suggestion. 想到一个简便算法，辛苦老师帮忙看看是否可以适用其他情况1.首先知道生活费需要是先付年金形式，调整计算器之后pmt=-100000，I/Y=-0.78,N=10,FV=0,算出pv=1036127.84由于是从第二年末inflation才开始调整的，所以I/Y=-0.78对应的调整之后的数据，而本身还有一年2.2%未计算进去，所以还需要再多除一个（1+2.2%）通过数据验证是没问题的，所以想看看这种取巧的方法能否在之后其他类似的题中推广，也就不存在理解起来比较费劲的问题了
NO.PZ201803130100000602 问题如下 Construtheoverall goals-baseasset allocation for the Armstrongs given their three goalsanAbbott’s suggestion for investing any excess capital. Show yourcalculations.Show your calculations. Guiline Answer:■ The mole thshoulselectefor eagois the one thoffers the highest return given the time horizon anrequireprobability of success.■ Approximately 16.4%, 12.7%, 50.4%, an20.5% shoulinvestein Moles an respectively. The appropriate goals-baseallocation for the Armstrongs is follows:Supporting calculations:For Go1, whiha time horizon of five years ana requireprobability of success of 85%, Mole C shoulchosen because its 4.4% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go1 is calculatefollows:N = 5, FV = –5,000,000, I/Y = 4.4%; CPT PV = $4,031,508 (or $4.03 million)So, approximately 50.4% of the totassets of $8 million (= $4.03 million/$8.00 million) shoulallocateto Mole For Go2, whiha time horizon of 10 years ana requireprobability of success of 99%, Mole B shoulchosen because its 2.2% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go2 is calculatefollows:PV=$100,000/(1.022)1+$100,000(1.03)1/(1.022)2+$100,000(1.03)2/(1.022)3+...+$100,000(1.03)9/(1.022)10PV = $1,013,670 (or $1.01 million)So, approximately 12.7% of the totassets of $8 million (= $1.01 million/$8.00 million) shoulallocateto Mole For Go3, whiha time horizon of 25 years ana requireprobability of success of 75%, Mole shoulchosen because its 7.5% expectereturn is higher ththe expectereturns of all the other moles. The present value ofGo3 is calculatefollows:N = 25, FV = –10,000,000, I/Y = 7.5%; CPT PV = $1,639,791 (or $1.64 million)So, approximately 20.5% of the totassets of $8 million (= $1.64 million/$8.00 million) shoulallocateto Mole Finally, the surplus of $1,315,032 (= $8,000,000 – $4,031,508 – $1,013,670 –$1,639,791), representing 16.4% (= $1.32 million/$8.00 million), shoulinvestein Mole A following Abbott’s suggestion. 1.这里的inflation rate 可以算到分母上去吗？还是一定要算到分子上？2.这里的折现率为什么可以直接用表格里的
NO.PZ201803130100000602 问题如下 Construtheoverall goals-baseasset allocation for the Armstrongs given their three goalsanAbbott’s suggestion for investing any excess capital. Show yourcalculations.Show your calculations. Guiline Answer:■ The mole thshoulselectefor eagois the one thoffers the highest return given the time horizon anrequireprobability of success.■ Approximately 16.4%, 12.7%, 50.4%, an20.5% shoulinvestein Moles an respectively. The appropriate goals-baseallocation for the Armstrongs is follows:Supporting calculations:For Go1, whiha time horizon of five years ana requireprobability of success of 85%, Mole C shoulchosen because its 4.4% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go1 is calculatefollows:N = 5, FV = –5,000,000, I/Y = 4.4%; CPT PV = $4,031,508 (or $4.03 million)So, approximately 50.4% of the totassets of $8 million (= $4.03 million/$8.00 million) shoulallocateto Mole For Go2, whiha time horizon of 10 years ana requireprobability of success of 99%, Mole B shoulchosen because its 2.2% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go2 is calculatefollows:PV=$100,000/(1.022)1+$100,000(1.03)1/(1.022)2+$100,000(1.03)2/(1.022)3+...+$100,000(1.03)9/(1.022)10PV = $1,013,670 (or $1.01 million)So, approximately 12.7% of the totassets of $8 million (= $1.01 million/$8.00 million) shoulallocateto Mole For Go3, whiha time horizon of 25 years ana requireprobability of success of 75%, Mole shoulchosen because its 7.5% expectereturn is higher ththe expectereturns of all the other moles. The present value ofGo3 is calculatefollows:N = 25, FV = –10,000,000, I/Y = 7.5%; CPT PV = $1,639,791 (or $1.64 million)So, approximately 20.5% of the totassets of $8 million (= $1.64 million/$8.00 million) shoulallocateto Mole Finally, the surplus of $1,315,032 (= $8,000,000 – $4,031,508 – $1,013,670 –$1,639,791), representing 16.4% (= $1.32 million/$8.00 million), shoulinvestein Mole A following Abbott’s suggestion. PV2 = 1067212 13.34% I/Y = （1+2.2%）/（1+3%）-1 = -0.78%PMT = 100000 * 1.03 = 103000N = 10FV = 0这为什么错了呢
NO.PZ201803130100000602 问题如下 Construtheoverall goals-baseasset allocation for the Armstrongs given their three goalsanAbbott’s suggestion for investing any excess capital. Show yourcalculations.Show your calculations. Guiline Answer:■ The mole thshoulselectefor eagois the one thoffers the highest return given the time horizon anrequireprobability of success.■ Approximately 16.4%, 12.7%, 50.4%, an20.5% shoulinvestein Moles an respectively. The appropriate goals-baseallocation for the Armstrongs is follows:Supporting calculations:For Go1, whiha time horizon of five years ana requireprobability of success of 85%, Mole C shoulchosen because its 4.4% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go1 is calculatefollows:N = 5, FV = –5,000,000, I/Y = 4.4%; CPT PV = $4,031,508 (or $4.03 million)So, approximately 50.4% of the totassets of $8 million (= $4.03 million/$8.00 million) shoulallocateto Mole For Go2, whiha time horizon of 10 years ana requireprobability of success of 99%, Mole B shoulchosen because its 2.2% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go2 is calculatefollows:PV=$100,000/(1.022)1+$100,000(1.03)1/(1.022)2+$100,000(1.03)2/(1.022)3+...+$100,000(1.03)9/(1.022)10PV = $1,013,670 (or $1.01 million)So, approximately 12.7% of the totassets of $8 million (= $1.01 million/$8.00 million) shoulallocateto Mole For Go3, whiha time horizon of 25 years ana requireprobability of success of 75%, Mole shoulchosen because its 7.5% expectereturn is higher ththe expectereturns of all the other moles. The present value ofGo3 is calculatefollows:N = 25, FV = –10,000,000, I/Y = 7.5%; CPT PV = $1,639,791 (or $1.64 million)So, approximately 20.5% of the totassets of $8 million (= $1.64 million/$8.00 million) shoulallocateto Mole Finally, the surplus of $1,315,032 (= $8,000,000 – $4,031,508 – $1,013,670 –$1,639,791), representing 16.4% (= $1.32 million/$8.00 million), shoulinvestein Mole A following Abbott’s suggestion. 老师，go2在求present value是 计算器有没有快捷算法，按照解析给的公式，考试根本不可能算出来。
NO.PZ201803130100000602问题如下Construtheoverall goals-baseasset allocation for the Armstrongs given their three goalsanAbbott’s suggestion for investing any excess capital. Show yourcalculations.Show your calculations. Guiline Answer:■ The mole thshoulselectefor eagois the one thoffers the highest return given the time horizon anrequireprobability of success.■ Approximately 16.4%, 12.7%, 50.4%, an20.5% shoulinvestein Moles an respectively. The appropriate goals-baseallocation for the Armstrongs is follows:Supporting calculations:For Go1, whiha time horizon of five years ana requireprobability of success of 85%, Mole C shoulchosen because its 4.4% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go1 is calculatefollows:N = 5, FV = –5,000,000, I/Y = 4.4%; CPT PV = $4,031,508 (or $4.03 million)So, approximately 50.4% of the totassets of $8 million (= $4.03 million/$8.00 million) shoulallocateto Mole For Go2, whiha time horizon of 10 years ana requireprobability of success of 99%, Mole B shoulchosen because its 2.2% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go2 is calculatefollows:PV=$100,000/(1.022)1+$100,000(1.03)1/(1.022)2+$100,000(1.03)2/(1.022)3+...+$100,000(1.03)9/(1.022)10PV = $1,013,670 (or $1.01 million)So, approximately 12.7% of the totassets of $8 million (= $1.01 million/$8.00 million) shoulallocateto Mole For Go3, whiha time horizon of 25 years ana requireprobability of success of 75%, Mole shoulchosen because its 7.5% expectereturn is higher ththe expectereturns of all the other moles. The present value ofGo3 is calculatefollows:N = 25, FV = –10,000,000, I/Y = 7.5%; CPT PV = $1,639,791 (or $1.64 million)So, approximately 20.5% of the totassets of $8 million (= $1.64 million/$8.00 million) shoulallocateto Mole Finally, the surplus of $1,315,032 (= $8,000,000 – $4,031,508 – $1,013,670 –$1,639,791), representing 16.4% (= $1.32 million/$8.00 million), shoulinvestein Mole A following Abbott’s suggestion. 如题irr是不是应该用每个portfolio 的expectereturn，而不是在特定年限和概率下的return
