$5,000 received each year for seven years on the last day of each year if your investments pay 7

Calculate the present value of the following annuity streams:

a. $5,000 received each year for seven years on the last day of each year if your investments pay 7 percent compounded annually.
b. $5,000 received each quarter for seven years on the last day of each quarter if your investments pay 7 percent compounded quarterly.
c. $5,000 received each year for seven years on the first day of each year if your investments pay 7 percent compounded annually.
d. $5,000 received each quarter for seven years on the first day of each quarter if your investments pay 7 percent compounded quarterly.

 

Save your time - order a paper!

Get your paper written from scratch within the tight deadline. Our service is a reliable solution to all your troubles. Place an order on any task and we will take care of it. You won’t have to worry about the quality and deadlines

Order Paper Now

Answer

a)

Present value = Annuity * [1 – 1 / (1 + r)n] / r

Present value = 5000 * [1 – 1 / (1 + 0.07)7] / 0.07

Present value = 5000 * [1 – 0.62275] / 0.07

Present value = 5000 * 5.389289

Present value = $26,946.45

b)

Number of periods = 7 * 4 = 28

Rate = 7% / 4 = 1.75%

Present value = Annuity * [1 – 1 / (1 + r)n] / r

Present value = 5000 * [1 – 1 / (1 + 0.0175)28] / 0.0175

Present value = 5000 * [1 – 0.615228] / 0.0175

Present value = 5000 * 21.986955

Present value = $109,934.48

c)

Present value =(1 + r) * Annuity * [1 – 1 / (1 + r)n] / r

Present value = (1 + 0.07) * 5000 * [1 – 1 / (1 + 0.07)7] / 0.07

Present value = 1.07 * 5000 * [1 – 0.62275] / 0.07

Present value = 1.07 * 5000 * 5.389289

Present value = $28,832.70

Number of periods = 7 * 4 = 28

Rate = 7% / 4 = 1.75%

Present value = (1 + r) * Annuity * [1 – 1 / (1 + r)n] / r

Present value = (1 + 0.0175) * 5000 * [1 – 1 / (1 + 0.0175)28] / 0.0175

Present value = 1.0175 * 5000 * [1 – 0.615228] / 0.0175

Present value = 1.0175 * 5000 * 21.986955

Present value = $111,858.63