Question

Calculate the present value of the following: a-1. Annual payment of $800 for 10 years at 5% interest. (Do not round intermediate calculations. Round your answer to 2 decimal places.) a-2. Annual payment of $600 for 15 years at 5% interest. (Do not round intermediate calculations. Round your answer to 2 decimal places.) a-3. Which option would you prefer? b-1. Annual payment of $800 for 10 years at 20% interest. (Do not round intermediate calculations. Round your answer to 2 decimal places.) b-2. Annual payment of $600 for 15 years at 20% interest. (Do not round intermediate calculations. Round your answer to 2 decimal places.) b-3. Which option would you prefer?

Answer 1

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

Step-by-step explanation:

a-1 describes an ordinary annuity whose present value is calculated as follows:

`Present value =PMT*([1-(1+i)^-^n])/(i)`

where PMT=$800; i= 5%, n= 10

`Present value =800*([1-(1+0.05)^-^1^0])/(0.05)` = 6,177.39

a2-
`Present value =600*([1-(1+0.05)^-^1^5])/(0.05)` = 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*([1-(1+0.20)^-^1^0])/(0.20)` = 3,353.98

b2-
`Present value =600*([1-(1+0.20)^-^1^5])/(0.20)` =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.