公式是如何推导的？

NO.PZ2020012005000020 问题如下 If a stoinx, interest rate, anvinyielremain constant, rive a formula for the futures pritime t in terms of the futures pritime zero. Suppose ththe risk-free rate is 5% per yeanthe vinyielon inx is 3% per year. If the stoinx stays constant, whrate es the futures prigrow? (All rates are expressewith annucompounng.) The relationship between the futures price, Ft, time t anthe spot priis:Ft=S(1+R1+Q)T−t=S(1+R1+Q)T(1+Q1+R)t=F0(1+Q1+R)tF_t=S(\frac{1+R}{1+Q})^{T-t}=S(\frac{1+R}{1+Q})^T(\frac{1+Q}{1+R})^t=F_0(\frac{1+Q}{1+R})^tFt​=S(1+Q1+R​)T−t=S(1+Q1+R​)T(1+R1+Q​)t=F0​(1+R1+Q​)twhere S, R, anQ are the inx level, risk-free rate, anvinyiel respectively anT is the inititime to maturity. This shows ththe futures prigrows at:(1 + Q)/( 1 + R)- 1When R = 5% anQ = 3%, the growth rate of the futures priper yeis(1 + Q)/( 1 + R)- 1=1.03/1.05-1=-0.019or -1.9%. 咱们这个题滴哩咕噜说了一大堆，是不是就是在说三个时间点的关系分别是0时刻，现货时刻（S表示的）F小t时刻的价格F大T终值时刻（蓝色F0吗）根据正常公式应该是rf在Q（vin头上，但是最后Q跑到R头上去了，所以是否蓝色F0 代表F大T时刻的价值，逆向复利t回来了t时刻？字母有点乱，我看不太懂了，很迷茫，麻烦解答一下我的理解思路是否有问题反正这个题目就是问中间的小t时刻的期货价值定价计算呗，绿色框框内的推导，最后一步我不太懂是干嘛的了。谢谢老师

NO.PZ2020012005000020 问题如下 If a stoinx, interest rate, anvinyielremain constant, rive a formula for the futures pritime t in terms of the futures pritime zero. Suppose ththe risk-free rate is 5% per yeanthe vinyielon inx is 3% per year. If the stoinx stays constant, whrate es the futures prigrow? (All rates are expressewith annucompounng.) The relationship between the futures price, Ft, time t anthe spot priis:Ft=S(1+R1+Q)T−t=S(1+R1+Q)T(1+Q1+R)t=F0(1+Q1+R)tF_t=S(\frac{1+R}{1+Q})^{T-t}=S(\frac{1+R}{1+Q})^T(\frac{1+Q}{1+R})^t=F_0(\frac{1+Q}{1+R})^tFt​=S(1+Q1+R​)T−t=S(1+Q1+R​)T(1+R1+Q​)t=F0​(1+R1+Q​)twhere S, R, anQ are the inx level, risk-free rate, anvinyiel respectively anT is the inititime to maturity. This shows ththe futures prigrows at:(1 + Q)/( 1 + R)- 1When R = 5% anQ = 3%, the growth rate of the futures priper yeis(1 + Q)/( 1 + R)- 1=1.03/1.05-1=-0.019or -1.9%. 请问题目中的pritime zero，指的是下图中左边的S0时刻还是右边的S0时刻，如果是右边的，那不是time t么

NO.PZ2020012005000020 问题如下 If a stoinx, interest rate, anvinyielremain constant, rive a formula for the futures pritime t in terms of the futures pritime zero. Suppose ththe risk-free rate is 5% per yeanthe vinyielon inx is 3% per year. If the stoinx stays constant, whrate es the futures prigrow? (All rates are expressewith annucompounng.) The relationship between the futures price, Ft, time t anthe spot priis:Ft=S(1+R1+Q)T−t=S(1+R1+Q)T(1+Q1+R)t=F0(1+Q1+R)tF_t=S(\frac{1+R}{1+Q})^{T-t}=S(\frac{1+R}{1+Q})^T(\frac{1+Q}{1+R})^t=F_0(\frac{1+Q}{1+R})^tFt​=S(1+Q1+R​)T−t=S(1+Q1+R​)T(1+R1+Q​)t=F0​(1+R1+Q​)twhere S, R, anQ are the inx level, risk-free rate, anvinyiel respectively anT is the inititime to maturity. This shows ththe futures prigrows at:(1 + Q)/( 1 + R)- 1When R = 5% anQ = 3%, the growth rate of the futures priper yeis(1 + Q)/( 1 + R)- 1=1.03/1.05-1=-0.019or -1.9%. 请问这道题用画图法怎么解

NO.PZ2020012005000020 问题如下 If a stoinx, interest rate, anvinyielremain constant, rive a formula for the futures pritime t in terms of the futures pritime zero. Suppose ththe risk-free rate is 5% per yeanthe vinyielon inx is 3% per year. If the stoinx stays constant, whrate es the futures prigrow? (All rates are expressewith annucompounng.) The relationship between the futures price, Ft, time t anthe spot priis:Ft=S(1+R1+Q)T−t=S(1+R1+Q)T(1+Q1+R)t=F0(1+Q1+R)tF_t=S(\frac{1+R}{1+Q})^{T-t}=S(\frac{1+R}{1+Q})^T(\frac{1+Q}{1+R})^t=F_0(\frac{1+Q}{1+R})^tFt​=S(1+Q1+R​)T−t=S(1+Q1+R​)T(1+R1+Q​)t=F0​(1+R1+Q​)twhere S, R, anQ are the inx level, risk-free rate, anvinyiel respectively anT is the inititime to maturity. This shows ththe futures prigrows at:(1 + Q)/( 1 + R)- 1When R = 5% anQ = 3%, the growth rate of the futures priper yeis(1 + Q)/( 1 + R)- 1=1.03/1.05-1=-0.019or -1.9%. 1.通过老师讲的定价公式能得出FP=S0(1+5%)^T/(1+3%)^T，请问这里的FP是指0时刻的FP吗？2.不懂题目的意思，也不明白答案中的计算。请老师一下。谢谢。