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%. 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。

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%.

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%. Fp. 增长率怎么计算？谢谢

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 + Q)/( 1 + R)- 1是怎么得出的？谢谢