Question

What is the the present value of $10,000 that you expect to receive in 10 years if the interest rate is 5% from years 0 to 5 and 7% from year 5 to 10? Show all work.

Answer 1

Year	Cash Flows	Discounting rate 5%for First 5 years 7% for next 5 years	Present Value (Discounting rate *Cash flows)
1	1000	.952	952
2	1000	.907	907
3	1000	.863	863
4	1000	.822	822
5	1000	.783	783
6	1000	.666	666
7	1000	.622	622
8	1000	.582	582
9	1000	.543	543
10	1000	.508	508
	TOTAL	=	$ 7248

In this case, It has been been assumed that the cash flows of $ 10000 have been recieved in equal installments in 10 years which makes a total of (10000/10)= $ 1000 Per year.

So the present value after these calculations are $ 7248

It has also been assumed that Cash flows streams are starting from end of Year 1 to end of year 10.

Then the cash flows have been discounted using 5% for first years and 7% for next 5 years . It makes a total of $ 7248 in 10 years

If say we have assumed that 10000 is received each year and there is 10000 received for 10 years then the overall cash flows would have been 72480 instead of 7248.