Question

Calculate the present value of the following annuity streams: a. $6,000 received each year for 6 years on the last day of each year if your investments pay 7 percent compounded annually. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) Present value $ b. $6,000 received each quarter for 6 years on the last day of each quarter if your investments pay 7 percent compounded quarterly. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) Present value $ c. $6,000 received each year for 6 years on the first day of each year if your investments pay 7 percent compounded annually. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) Present value $ d. $6,000 received each quarter for 6 years on the first day of each quarter if your investments pay 7 percent compounded quarterly. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Answer 1

Annuity is fixed cashflows with fixed intervals

PV of Annuity = P [ 1 - (1+r)^-n ] / r

where p is Periodic payment

r is rate per period

n is no.of periods

1.

PV of Annuity = P [ 1 - (1+r)^-n ] / r

= $ 6,000 [ 1-(1+0.07)^-6] / 0.07

= $ 6,000 [ 1-(1.07)^-6] / 0.07

= $ 6,000 [ 1-0.6663] / 0.07

= $ 6,000 [ 1-0.6663] / 0.07

= $ 6,000 [ 0.3337] / 0.07

= $ 28,602.86

2.

PV of Annuity = P [ 1 - (1+r)^-n ] / r

= $ 6,000 [ 1-(1+0.0175)^-24] / 0.0175

= $ 6,000 [ 1-(1.0175)^-24] / 0.0175

= $ 6,000 [ 1-0.6594] / 0.0175

= $ 6,000 [0.3406] / 0.0175

= $ 116,777.14

3. If cash flows are received in the begining of period

PV of Annuity = [P [ 1 - (1+r)^-n-1 ] / r] + periodic payment

= {$ 6,000 [ 1-(1+0.07)^-5] / 0.07} + $ 6,000

= {$ 6,000 [ 1-(1.07)^-5] / 0.07} + $ 6,000

= {$ 6,000 [ 1-0.7130] / 0.07} + $ 6,000

= {$ 6,000 [ 0.2870 ] / 0.07} + $ 6,000

= $ 24,600 + $ 6,000

= $ 30,600

4. If the cash flows are received at the begining of the period

PV of Annuity = {P [ 1 - (1+r)^-n-1 ] / r} + Periodic payment

= {$ 6,000 [ 1-(1+0.0175)^-24-1] / 0.0175} + $ 6,000

= {$ 6,000 [ 1-(1.0175)^-23] / 0.0175} + $ 6,000

= {$ 6,000 [ 1-0.6710] / 0.0175} + $ 6,000

= {$ 6,000 [0.3290] / 0.0175} + $ 6,000

= $ 112,800 + $ 6,000

= $ 118,800