Question

​(Related to Checkpoint​ 6.2)  ​(Present value of annuity​ payments)  The state​ lottery's million-dollar payout provides for

​$1.3

million to be paid in

25

installments of

​$52,000

per payment. The first

​$52,000

payment is made​ immediately, and the

24

remaining

​$52,000

payments occur at the end of each of the next

24

years. If

8

percent is the discount​ rate, what is the present value of this stream of cash​ flows? If

16

percent is the discount​ rate, what is the present value of the cash​ flows?

a.  If

8

percent is the discount​ rate, the present value of the annuity due is

​$nothing.

​(Round to the nearest​ cent.)

Answer 1

- Equal Annual 25 Installment of lottery payment = $52,000

The first ​$52,000 payment is made​ immediately, and the 24 remaining ​$52,000 payments occur at the end of each of the next 24 years which means that 25 payments will be made in 24 years.

To Calculate the Present value we will due ordinary annuity due formula for the last 24 payments and will add to it the1st payment which is made today.  

a).Calculating the Present Value If 8 percent is the discount​ rate:-

Where, C= Periodic Payments = $52,000

r = Periodic Interest rate = 8%

n= no of periods = 24 years

Present Value = $599,495.43

So, the present value of this stream of cash​ flows is $599,495.43

b).Calculating the Present Value If 16 percent is the discount​ rate:-

Where, C= Periodic Payments = $52,000

r = Periodic Interest rate = 16%

n= no of periods = 24 years

Present Value = $367,776.59

So, the present value of this stream of cash​ flows is $367,776.59

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