一道题

NO.PZ2022070602000014 问题如下 The treasurer of a Lonn-baseinsurancompany expects th3 years from toy the company will receive G800,000. The treasurer plans to invest the fun for 1 yeafter thancis to loin a rate of return on the fun toy’s forwarrate for the perio The current 3-yean4-yespot rates are 1.5% an2% respectively, anthe company cborrow anlenthese rates. Assuming continuous compounng, how muinterest income will the company earn in the 1-yeperiobeginning 3 years from toy, anwhtransactions shoulthe treasurer enter into toy in orr to loin this return? A.Borrow the 3-yespot rate anlenthe 4-yespot rate to earn a return of G28,000. B.Lenthe 3-yespot rate anborrow the 4-yespot rate to earn a return of G28,000. C.Borrow the 3-yespot rate anlenthe 4-yespot rate to earn a return of G28,119. Lenthe 3-yespot rate anborrow the 4-yespot rate to earn a return of G28,119. 中文解析A正确。从第3年年末至第4年年末的远期利率 F=R2T2−R1T1T2−T1F=\frac{R_{2} T_{2}-R_{1} T_{1}}{T_{2}-T_{1}}F=T2​−T1​R2​T2​−R1​T1​​=0.02∗4−0.015∗34−3=0.035 or 3.5%=\frac{0.02 * 4-0.015 * 3}{4-3}=0.035 \text { or } 3.5 \%=4−30.02∗4−0.015∗3​=0.035 or 3.5%或者，𝐹 = 𝑙𝑛(𝑒𝑥𝑝(0.02 ∗ 4)/𝑒𝑥𝑝(0.015 ∗ 3)).英镑3.5%的利率等价于在第1年有28000英镑。为了获得这些利息，公司需要现在借入800000英镑，用1.5%的利率借3年期，并且把钱用2%的利率投资4年。---------------------------------------------------------------------------------------------------------------------------------A is correct. The forwarrate for the periofrom the enof ye3 to the enof ye4 is:F=R2T2−R1T1T2−T1F=\frac{R_{2} T_{2}-R_{1} T_{1}}{T_{2}-T_{1}}F=T2​−T1​R2​T2​−R1​T1​​=0.02∗4−0.015∗34−3=0.035 or 3.5%=\frac{0.02 * 4-0.015 * 3}{4-3}=0.035 \text { or } 3.5 \%=4−30.02∗4−0.015∗3​=0.035 or 3.5%Alternatively, 𝐹 = 𝑙𝑛(𝑒𝑥𝑝(0.02 ∗ 4)/𝑒𝑥𝑝(0.015 ∗ 3)).3.5% interest on the G800,000 investeequals G28,000 in 1 year. To earn thisinterest, the company woulneeto borrow G800,000 toy 1.5% for 3 years annvest the procee 2% for 4 years.B is incorrect. The company nee to borrow the 3-yespot rate anlenthe 4-yespot rate.C anare incorrect. G28,119 is the interest income if annucompounng is usensteof continuous compounng 应该借短投长，借三年的钱投四年，这个我明白，但是收益没看懂为什么是这么算的。80万投四年的收益是800000*e^(0.02*4)，其中三年的借款成本是800000*e^(0.015*3)，二者相减=29807.4。这个思路哪里有问题？

NO.PZ2022070602000014 问题如下 The treasurer of a Lonn-baseinsurancompany expects th3 years from toy the company will receive G800,000. The treasurer plans to invest the fun for 1 yeafter thancis to loin a rate of return on the fun toy’s forwarrate for the perio The current 3-yean4-yespot rates are 1.5% an2% respectively, anthe company cborrow anlenthese rates. Assuming continuous compounng, how muinterest income will the company earn in the 1-yeperiobeginning 3 years from toy, anwhtransactions shoulthe treasurer enter into toy in orr to loin this return? A.Borrow the 3-yespot rate anlenthe 4-yespot rate to earn a return of G28,000. B.Lenthe 3-yespot rate anborrow the 4-yespot rate to earn a return of G28,000. C.Borrow the 3-yespot rate anlenthe 4-yespot rate to earn a return of G28,119. Lenthe 3-yespot rate anborrow the 4-yespot rate to earn a return of G28,119. 中文解析A正确。从第3年年末至第4年年末的远期利率 F=R2T2−R1T1T2−T1F=\frac{R_{2} T_{2}-R_{1} T_{1}}{T_{2}-T_{1}}F=T2​−T1​R2​T2​−R1​T1​​=0.02∗4−0.015∗34−3=0.035 or 3.5%=\frac{0.02 * 4-0.015 * 3}{4-3}=0.035 \text { or } 3.5 \%=4−30.02∗4−0.015∗3​=0.035 or 3.5%或者，𝐹 = 𝑙𝑛(𝑒𝑥𝑝(0.02 ∗ 4)/𝑒𝑥𝑝(0.015 ∗ 3)).英镑3.5%的利率等价于在第1年有28000英镑。为了获得这些利息，公司需要现在借入800000英镑，用1.5%的利率借3年期，并且把钱用2%的利率投资4年。---------------------------------------------------------------------------------------------------------------------------------A is correct. The forwarrate for the periofrom the enof ye3 to the enof ye4 is:F=R2T2−R1T1T2−T1F=\frac{R_{2} T_{2}-R_{1} T_{1}}{T_{2}-T_{1}}F=T2​−T1​R2​T2​−R1​T1​​=0.02∗4−0.015∗34−3=0.035 or 3.5%=\frac{0.02 * 4-0.015 * 3}{4-3}=0.035 \text { or } 3.5 \%=4−30.02∗4−0.015∗3​=0.035 or 3.5%Alternatively, 𝐹 = 𝑙𝑛(𝑒𝑥𝑝(0.02 ∗ 4)/𝑒𝑥𝑝(0.015 ∗ 3)).3.5% interest on the G800,000 investeequals G28,000 in 1 year. To earn thisinterest, the company woulneeto borrow G800,000 toy 1.5% for 3 years annvest the procee 2% for 4 years.B is incorrect. The company nee to borrow the 3-yespot rate anlenthe 4-yespot rate.C anare incorrect. G28,119 is the interest income if annucompounng is usensteof continuous compounng 公司需要现在借入800000英镑，用1.5%的利率借3年期，并且把钱用2%的利率投资4年，这些操作就是为了锁定3.5%的远期利率吗？