Answer:
a-1 Present value = 6,177.39
a2- Present Value =6,227.79
a3- Choose the payment stream with the highest present value = a2
b1- Present Value=3,353.98
b2-Present Value=2,805.28
b3-Choose the payment stream with the highest present value = b1
Explanation:
a-1 describes an ordinary annuity whose present value is calculated as follows:
![Present value =PMT*\frac{[1-(1+i)^-^n]}{i}](https://tex.z-dn.net/?f=%20Present%20value%20%3DPMT%2A%5Cfrac%7B%5B1-%281%2Bi%29%5E-%5En%5D%7D%7Bi%7D)
where PMT=$800; i= 5%, n= 10
![Present value =800*\frac{[1-(1+0.05)^-^1^0]}{0.05}](https://tex.z-dn.net/?f=%20Present%20value%20%3D800%2A%5Cfrac%7B%5B1-%281%2B0.05%29%5E-%5E1%5E0%5D%7D%7B0.05%7D) = 6,177.39
 = 6,177.39
a2- ![Present value =600*\frac{[1-(1+0.05)^-^1^5]}{0.05}](https://tex.z-dn.net/?f=Present%20value%20%3D600%2A%5Cfrac%7B%5B1-%281%2B0.05%29%5E-%5E1%5E5%5D%7D%7B0.05%7D) = 6,227.79
 = 6,227.79
a3- If I were receiving these payments annually, I would prefer the payment stream with the highest present value ie a2 -Annual payment of $600 for 15 years at 5% interest.
b1- ![Present value =800*\frac{[1-(1+0.20)^-^1^0]}{0.20}](https://tex.z-dn.net/?f=Present%20value%20%3D800%2A%5Cfrac%7B%5B1-%281%2B0.20%29%5E-%5E1%5E0%5D%7D%7B0.20%7D) = 3,353.98
 = 3,353.98
b2-![Present value =600*\frac{[1-(1+0.20)^-^1^5]}{0.20}](https://tex.z-dn.net/?f=Present%20value%20%3D600%2A%5Cfrac%7B%5B1-%281%2B0.20%29%5E-%5E1%5E5%5D%7D%7B0.20%7D) =2,805.28
 =2,805.28
b3- f I were receiving these payments annually, I would prefer the payment stream with the highest present value ie b1- Annual payment of $800 for 10 years at 20% interest.