Question

Calculate the present value of the following annuity streams:

a. $5,000 received each year for 7 years on the last day of each year if your investments pay 7 percent compounded annually.
b. $5,000 received each quarter for 7 years on the last day of each quarter if your investments pay 7 percent compounded quarterly.
c. $5,000 received each year for 7 years on the first day of each year if your investments pay 7 percent compounded annually.
d. $5,000 received each quarter for 7 years on the first day of each quarter if your investments pay 7 percent compounded quarterly.
  
(For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

Answer 1

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