Question

1. The following questions relate to the concept of present value.
   
   a. Find the present value of $1000 to be paid 3 years in the future if the interest rate is 5%.
   
   b. Find the present value of $1000 to be paid in 5 years in the future if the interest rate is 5%?
   
   c. What do you notice about the relationship between time and present value? The further into the future a payment (or event) occurs, what happens to the present value?
   
   d. Find the present value of $1000 to be paid 3 years in the future if the interest rate is 10%.
   
   e. What is the relationship between the interest rate and present value? What happens to present value of a payment (or event) if we use a higher interest rate?

Answer 1

To calculate present value we use formula

PV = FV / (1+i)^t

where i is interest rate and t is time

a) FV = 1000, i =5% = 0.05, t = 3yrs

PV = 1000 / (1+0.05)^3

= 1000 / 1.05^3 = 863.837 = 863.84

b) FV = 1000, i =5% = 0.05, t = 5yrs

PV = 1000 / (1+0.05)^5

= 1000 / 1.05^5 = 783.526 = 783.53

c) there is a inverse relationship between time and present value. the further into the future payment occur, the less is the present value of the payment. (783.53<863.84)

d) FV = 1000, i =10% = 0.1, t = 3yrs

PV = 1000 / (1+0.1)^3

= 1000 / 1.1^3 = 751.31

e) there is a inverse relationship between interest rate and present value. the more interest rate, the less is the present value of the payment. (751.31<863.84)