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

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:

$Present value =PMT*\frac{[1-(1+i)^-^n]}{i}$

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

$Present value =800*\frac{[1-(1+0.05)^-^1^0]}{0.05}$ = 6,177.39

a2- $Present value =600*\frac{[1-(1+0.05)^-^1^5]}{0.05}$ = 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- $Present value =800*\frac{[1-(1+0.20)^-^1^0]}{0.20}$ = 3,353.98

b2-$Present value =600*\frac{[1-(1+0.20)^-^1^5]}{0.20}$ =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.