I just spent two hours on this and I'm certain I'm off. Any help getting me on track will be greatly appricated.


Question:
How much would you have to invest today to receive.

a. $15,000 in 8 years at 10 percent?

$15,000 / .467 = $32,119.14
$32,119.14 / 2.144 = $14,981.30

b. $20,000 in 12 years at 13 percent?

$20,000 / .231 = $86,580.08
$86,580.08 / 4.335 = $19,972.34

c. $6,000 each year for 10 years at 9 percent?

$14,200 / 2.367 = $5,999.16

d. $50,000 each year for 50 years at 7 percent?

1,473,000 / 29.457 = $50,005.09

Question:
How much would you have to invest today to receive.

a. $15,000 in 8 years at 10 percent?

$15,000 / .467 = $32,119.14
$32,119.14 / 2.144 = $14,981.30

This can be done two ways if you have the charts:
Future value = FV factor x Present Value
Present value = PV factor x Future Value

Since you're solving for present value, obviously the second one would be easier. You can do it the top way, but that means the division to work it backwards.

The 2.144 is the FV factor and the .467 is the PV factor. So you either:
15,000/2.144
OR 15,000 x .467

Not both. That 32 thousand doesn't even exist.

The .467 and 2.144 are just recipricals of each other. 1/2.144 = .467. :-)

You're applying them in an incorrect way, and trying to use both and combine them. In other words, you're actually making this difficult by trying to throw a division in there at all, because it's not even necessary.

Do this the easy way. You're solving for a present value. You want to know what you need today in order to grow into 15,000 in the future. Therefore, use the present value chart and PV factor and just multiply.



b. $20,000 in 12 years at 13 percent?

$20,000 / .231 = $86,580.08
$86,580.08 / 4.335 = $19,972.34

Basically, same thing here. 20,000 x .231. That's PV factor to get the present value.



c. $6,000 each year for 10 years at 9 percent?

$14,200 / 2.367 = $5,999.16

There are three errors here. First of all, it's an annuity. "each year" means you have a series of payments of 6000 each, for 10 total payments. A series of payments is an annuity. You're using the present value of $1 chart instead of the annuity chart. (Could be called "at the end of x periods" or "series of payments," and not necessarily "annuity." But the number should be 6.418 - find the number and you'll have the right chart.)

Second, it's not a division. You can't do these that way. You don't ever use PV and FV together on an annuity. The only time there would be a division is if you were trying to solve for the payment itself, but you aren't.

Third, where did the 14,200 come from? You multiply the factor by the payment. The chart will work out the fact that there are 10 payments. I don't get the 14,200 at all.



d. $50,000 each year for 50 years at 7 percent?

1,473,000 / 29.457 = $50,005.09

Ditto.