What is the value today of $5,000 per year, at a discount rate of 9 percent, if the first payment is

What is the value today of $5,000 per year, at a discount rate of 9 percent, if the first payment is received 5 years from today and the last payment is received 15 years from today? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

 

Value today

$

Explanation:

We want to find the value of the cash flows today, so we will find the PV of the annuity, and then bring the lump sum PV back to today. The annuity has 11 payments, so the PV of the annuity is:

  

PVA = $5,000{[1 – (1/1.0911)] / 0.09} = $34,025.95

  

Since this is an ordinary annuity equation, this is the PV one period before the first payment, so this is the PV at t = 4. To find the value today, we find the PV of this lump sum. The value today is:

  

PV = $34,025.95 / 1.094 = $24,104.84

   

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

   

Enter

11

9%

$5,000

N

I/Y

PV

PMT

FV

Solve for

$34,025.95

    

Enter

4

9%

$34,025.95

N

I/Y

PV

PMT

FV

Solve for

$24,104.84