I am working on a time value of money module for my intermediate accounting II class and it has been a while since I have used any financial tables so I am asking for a bit of feed back on what I have accomplished. I am having a few issues with Future Value.

The first question was:
What is the future value on December 31, 2016 of 10 cash flows of 20,000 with the first cash payment made on December 31, 2007 and interest at 10% being compounded annually.

I found this answer by using the Future value of an ordinary annuity of 1.

10 payments or years at 10% or 15.937425 * 20000
or 318748.5
I am fairly confident in this answer.

The next question is:

What is the future value on December 31, 2016 of 20 cash flows of 15,000 with the first cash payment made on December 31, 2007 and interest at 10% being compounded semi-annually.

Again i used the Future value of an ordinary annuity of 1.
This time i took 20 payments at 5% since we are paying semi-annually
15000 * 33.065954
or 495989.31

However the next question is making me second guess what I have done so far:
What is the future value on June 30, 2016 of 20 cash flows of 15,000 with the first cash payment made on December 31, 2007 and interest at 10% being compounded semi-annually. I tried making a table to get the correct answer because at first I was unsure of how to solve this problem. The answer I came up with was 480,989.31 this can't be right because in 6 months I will be adding the 20th payment of 15000 + interest earned and that will account for more money then my second answer. No sure what I am doing here lol.

Should is use the FV table again and do it by 19 cash flows? So my answer would look like
15000*458085.06 or (15000*30.539004)

First one is correct.


What is the future value on December 31, 2016 of 20 cash flows of 15,000 with the first cash payment made on December 31, 2007 and interest at 10% being compounded semi-annually.

Again i used the Future value of an ordinary annuity of 1.
This time i took 20 payments at 5% since we are paying semi-annually
15000 * 33.065954
or 495989.31

The problem is a little screwy. Your process is correct, factor correct. However, it's impossible to make 20 payments during that time if the first payment isn't until 12/31/07! It has to made on 6/30/07 for that work. If we assume someone's quality control on the question just isn't right and that first payment is 6/30/07, then you're correct. You always need to work in compounding periods.


However the next question is making me second guess what I have done so far:

What a coincidence. It's making me question that second one and what they really meant. (The first one's correct though because you don't have to worry about the semi-annual thing.)


What is the future value on June 30, 2016 of 20 cash flows of 15,000 with the first cash payment made on December 31, 2007 and interest at 10% being compounded semi-annually.

Should is use the FV table again and do it by 19 cash flows? So my answer would look like
15000*458085.06 or (15000*30.539004)

Very weird problems. Why are they talking about 20 cash flows if they aren't going to include all the cash flows? That's just confusing. Actually, it would be 18 payments, not 19, but you've got the right idea. There isn't a payment on 6/30/07. It's like saying you started this investment, whatever it is, on 6/30/07 and it's ending on 6/30/17. That's the only way to have 20 cash flows (10 full years), and make the first payment on 12/31/07. When 6/30/16 hits, you have two payments missing, not one.

(Just as a note, 15,000*458085.06 makes no sense. Is that a typo?)

Using that info, if we now return to that second one, that too would have to start 6/30/07 and end 6/30/17. In which case, only one payment is missing and you'd use 19. (i.e. the way you did the 3rd one)

I can think of some real-life examples of why you might want to do this, but this set-up for a problem just seems really whacky to me.