Part 1: Using the annual interest rate of 4 percent (i.e., r = .04), calculate t

Question

Part 1: Using the annual interest rate of 4 percent (i.e., r = .04), calculate the present values (at t = 0) for the following payments:

a. $1,000,000 at t = 1

b. $1,000,000 at t = 2

c. $1,000,000 at t = 3

Is the present value of $1,000,000 at t = 2 larger than, smaller than, or equal to the average of the present values of $1,000,000 at t = 1 and $1,000,000 at t = 3?

Part 2: Next calculate the present values of $1,000,000 at t = 3 for the following interest rates:

a. r = .10 (10%)

b. r = .15 (15%)

c. r = .20 (20%)

Is the present value of $1,000,000 at t = 3 with r = .15 larger than, smaller than, or equal to the average of the present values using r = .10 and r = .20?

Explanation / Answer

PArt 1:

a) PV= 1000000/1.04= $ 961538.46

b) PV= 1000000/1.04^2= $ 924556.213

c) PV= 1000000/1.04^3= $ 888996.359

the present value of $1,000,000 at t = 2 is SMALLER thanthe average of the present values of $1,000,000 at t = 1 and $1,000,000 at t = 3

PArt 2:

a) PV= 1000000/1.1^3= $ 751314.8

b) PV= 1000000/1.15^3= $ 657516.23

c) Pv= 1000000/1.20^3= $ 578703.704

the present value of $1,000,000 at t = 3 with r = .15 is SMALLERthanthe average of the present values using r = .10 and r = .20

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