I'm really struggling with how to work out the Present value. Any help would be appreciated!

Amount in future = £80,000.
Number of yrs = 23.
Rate of interest per year = 7%.

Calculate the present value.


I have a handout which has the discount factors but it only goes up to 15 yrs... just wondering what I do for 23 yrs?

The present value is :- £ 16,875.86.


Amount in future = £80,000.
Number of yrs = 23.
Rate of interest per year = 7%.


1 1.0000 1.0700
2 1.0700 1.1449
3 1.1449 1.2250
4 1.2250 1.3108
5 1.3108 1.4026
6 1.4026 1.5007
7 1.5007 1.6058
8 1.6058 1.7182
9 1.7182 1.8385
10 1.8385 1.9672
11 1.9672 2.1049
12 2.1049 2.2522
13 2.2522 2.4098
14 2.4098 2.5785
15 2.5785 2.7590
16 2.7590 2.9522
17 2.9522 3.1588
18 3.1588 3.3799
19 3.3799 3.6165
20 3.6165 3.8697
21 3.8697 4.1406
22 4.1406 4.4304
23 4.4304 4.7405

80,000.00 16,875.86

To find present value you consider the compound interest formula

A=P(1+r/n)^nt A= 80,000 R=7% T=23 years: your trying to solve for P
*N= # of compoundind periods(since you didn't write in I'm calling it "u")

Instead of memorizing a formula for present value, its better if you just derive it..

A=P(1+r/n)^nt < look at this formula.. to solve for p divide both sides by (1+r/n)^nt

this leaves you with A/(1+r/n)^nt= p or because the parenthesis part of the equation is in the denominator you bring it up with its negative power like this: P= A(1+r/n)^-nt (note: 3^-2 = 1/3^2)

Therefore P = 80,000[(1+0.07/u)^-(u*23)

your trying to solve for P
*N= # of compoundind periods(since you didn't write in I'm calling it "u")

Huh? Principle times the number of compounding periods is what you're solving for? So if my principle is 10,000 and I am compounding quarterly, this means that 10,000 * 4 means something?

You're way off track on that one. And she's not solving for anything to do with compounding periods cause she's already got that. And u is nothing, especially since P * N means nothing. Except in your equation below you're using u as n. So it's not what you said it was and you're changing the variable for no reason.


this leaves you with A/(1+r/n)^nt= p or because the parenthesis part of the equation is in the denominator you bring it up with its negative power like this: P= A(1+r/n)^-nt (note: 3^-2 = 1/3^2)

Therefore P = 80,000[(1+0.07/u)^-(u*23)

What is the point of making it this complicated? If she couldn't solve the original equation you gave, she certainly isn't solving this with some negative exponent in it. I had difficulty following this and I know how to do it. And why are you adding that u into it? If it hasn't given a compounding period, it's 1, so leaving it as a variable makes no sense and adds another complication that doesn't need to be there.

Not to mention that you haven't said what any of the variables stand for.

OK, I get it now. You were using the * as a footnote. That was VERY confusing and not at all obvious. You didn't put a * next to the N in the equation, so it just looks like you are multiplying P * N. Very unclear.

But the rest of my comments stand. There's still no reason to change it to a u, and no reason to be solving for it. If I'm confused, I'm certain OP is.

MaryLou, they should have given you some way to solve these without charts if your charts don't cover the numbers you need. However, there are three other ways to do them: algebra equations, Excel, and on a financial calculator. Are you required to use one of these, or can you do what you want?

The equation is:

FV=PV(1+i)^n


Where:
FV = future value or maturity value
PV = present value or principle
i = interest per compounding period
n = number of compounding periods

Because your problem compounds annually, you do not have to do any adjustments for the interest or time. So your i will equal your r (rate), and your n will equal your t (time).

So you would have:

80,000\ =\ PV\ (1\ +\ .07)^{23}

Can you solve for PV using algebra? (Do parenthesis first, followed by exponent. You'll then have it down where you can just divide both sides by that answer.)

If you hate that, you can flip it around and it becomes:

P = \frac{80,000}{(1\ +\ .07)^{23}}

Of course, you still have to solve everything on the bottom, and then divide 80,000 by that answer. It requires the same math and order as the one above. Unless you like doing negative exponents... But you don't need to solve for "u." It's 1.

A financial calculator will use the variables a bit differently. N will likely be total number of periods, and it'll have a period per year - in this case that is 1. It's compounding annually, so 1 period in the year.

See how you do with this. I haven't gone into what you do if you compound quarterly, monthly, etc. cause it complicates it and you don't need it for this problem. If you want to take that a step further, that can be done.

morgaine300,

The simplest is EXCEL!

By the way it is PRINCIPAL not PRINCIPLE.

Rolcam.

Sure, if they know how to use Excel. I don't do these in Excel, so I can't explain that to anyone, so don't expect me to. Besides, I didn't even originally post on this thread -- I was just trying to re-explain the other post, that's all.

And I really wish people would stop worrying about how I spell principal vs principle. I KNOW the difference - just because I rarely make typos or misspell things doesn't mean I can't do it sometimes, like when I don't feel like thinking about it. I think my occasional spelling mishaps is the last thing on earth anyone needs to worry about.