[camaroracr21]

the wording of this questions has me all confused. I do not even know where to start :(

The four numbers below are interest factors for future value of $1, present value of $1, future value of annuity of $1, and present value of annuity of $1 for the same interest rate and the same number of periods. Which one is most likely the future value of $1?
A) 1.17057
B) 0.85428
C) 4.55367
D) 5.33040

[morgaine300]

That's the first time I've seen a question ask you to try to relate the types of factors to which thing it is. Once you get experienced with it, it's a little easier to do that. Like I knew immediately which one it is, simply because it makes the "most" sense (and there's one answer that simply cannot be correct).

First, the present value of $1 and future value of $1 do not involve a series of payments. They involve a lump sum amount that happens only once. That is, you take say $1000 and stick it into something that earns interest and at the end of some period it's worth more. But you never put anything of your own into it again - you just earn interest.

This scenario involves both a present value and a future value. The present value always starts smaller, and then grows with interest over time, so that the future value is the bigger number. The factor from the chart you want is the one you're solving for.

So if you have $1000 today and stick it into something at 5% for a year, you want to solve for the future value, the unknown, what it will grow into. Look on your chart for future value of $1. Look under 5% for 1 year. Look at the kind of number it is. It's 1.05, because you would multiply by .05 to get the interest, but 1.05 means you're including the original principal. If you do it for 2 years, it'll be a little bit bigger. Look at the 5% for 2 years - it's just a bit bigger. Look at 3 years.

Now, what if instead I need to have $1000 a year from now, and I need to know what amount I would need today in order to grow to $1000. That means I'm solving for a present value. Look at the present value of $1 and look at the kind of numbers on that chart. The amount I would need today is smaller than my future amount - remember a present grows into a bigger future. So the numbers on this chart will bring your $1000 back to a small value for the present value.

From just doing these two, you should already be able to definitely eliminate one answer because it's impossible.

Now, an annuity is when payments are involved. Instead of just putting $1000 into an investment and letting it earn interest, you are going to put $1000 into it every year for the next 5 years. That means you're going to put $5000 in it total. Do you see that? So to see what it will be worth in the future, we can't just figure out what the interest would be -- we also have to include all those payments we're going to put into it. If I do it 2 years, I'll have put $2000 in, if for 3 years, $3000, etc. Look at the chart for future value of an annuity. Look at the kinds of numbers on there. That's because this is accounting for all those payments that would get put into the thing, in addition to the normal interest.

The present value of an annuity still involves payments. The difference is that you have an amount today but you're going to take payments off it until it's gone. But in the meantime it will still earn interest. So let's say you start with $5000 and you take $1000 out of it every year for 5 years. It earns interest, which makes it grow, you take $1000 out, leave $4000 plus some interest. The $4000 continues to earn interest, etc. So even though the payments you're taking out are only $1000, somewhere it was originally worth $5000. So our present value factor still has to be big enough to account for that and not just some interest. Look at the present value of an annuity table.

You don't have to know where those specific numbers came from - that is, you don't need to know the time or interest rate. Using 5% as an example should work. But can you now pick out one that would be the best choice for the future value of $1 (a non-annuity)?

[camaroracr21]

After looking at the charts, I believe you can eliminate b) 0.85428 and I believe the answer will be a) 1.17057. Sound correct?

[ArcSine]

Yep, assuming that the interest rate / discount rate is positive, then the FV of 1 will always be greater than 1, so (B) is eliminated right out of the gate.

Next, keeping the rate and holding period equal, the FV of an annuity of 1 will always* be greater than the FV of 1. Hence, the FV of 1 can't be the largest of the choices. (D)'s out.

*(except under some really weird conditions that you'd never encounter in the wild.)

As to picking between (A) and (C), I think your intuition--as honed by Morgaine's nice tutorial--is leading you to the right one.

Memo to Morgaine: I tried to send a greenie your way for that cool bit of explanation and analysis, but I was informed that my money's no good here (not 'til I spend a few coins elsewhere first).

[morgaine300]

Ah, gee, and I just left you one. Can't make change, huh? A great way to spend some coins is at the pub. :-)

But thanks anyway.

[ArcSine]

Aye... and first round's on me.