Question

What is the Present Value of the following cash flows at an interest rate of 7% AER? A.) $900 received one year from now. B.) $900 received 10 years from now. C.) $900 received each year beginning 1 year from now and ending in 10 years. D.) $900 received each year beginning 1 year from now and continuing forever.

Answer 1

Answer:

A.) $900 received one year from now.

$841.12

B.) $900 received 10 years from now.

$457.51

C.) $900 received each year beginning 1 year from now and ending in 10 years.

$6321.22

D.) $900 received each year beginning 1 year from now and continuing forever.

$12,857.14

Explanation:

Interest Rate = 7%

A.)

Cash flow = $900

Period = 1 year

PV  = FV / ( 1 + r )^n

PV  = $900 / ( 1 + 0.07 )^1

PV = $900 / 1.07

PV  = $841.12

B.)

Cash flow = $900

Period = 10 year

PV  = FV / ( 1 + r )^n

PV  = $900 / ( 1 + 0.07 )^10

PV = $900 / 1.96715

PV  = $457.51

C.)

Cash flow = $900

Period = 10 year

P  = [ r x PV / 1 - ( 1 + r )-n]

$900  = [ 0.07 x PV / 1 - ( 1 + 0.07 )-10]

$900  = [ 0.07 x PV / 1 - ( 1.07 )-10]

PV = ( $900 x 0.491651 ) / 0.07

PV = $6321.22

D.)

Cash flow = $900

Period = 10 year

PV = Pmt / i

PV = $900 / 0.07

PV  = $12,857.14