Finance Question - 20 bucks via paypal to the first one who answers it!
 

Ok,

The question is regarding the time value of money. I need to know which is more valuable, why and what formula was used to determine the answer.

A. 2,250 dollars a month for 40 years.
B. 2,750 dollars a month for 18 years.

Use 8% as an interest rate and tell me what each contract is worth today in a lump sum.

One of your advertisers wants to pay for a banner 40 years up front to get a better deal?

i'll take B

damn. I'm so bad at math.

compound interest?

Is this a test?


:1orglaugh

The Answer is A

the formula is im too lazy to do it and i have a 50/50 chance

b :thumbsup

if i was sitting for a grade 12 exam i could do it but the brain just cant be bothered even trying that sort of shit these days.

damn, I dont understand the question, but I know how to solve if I understood it 100%

LOL I wish.

I could tell you B is worth half as less as A

without interest A is over 1 Mil, and b is 550,000

Someone needs to reverse the compound interest. What don't you understand?

No shit, Sherlock.

B

Here is my formula...

Since your birth was at 1972 according to records you age must be x=2003-1972 which makes the x=31

So we have

x=31;
y=18;
z=40

if (x+y)<(x+z) { echo "At least you will have some time to spend profit"; } else { echo "Do you want that money for your grand sons to spend?"; }

:Graucho

In order to figure the time value of money you need a number to use for inflation right?

I like that!

Dude, I might just send you 20 dollars anyway.

In a perfect world you are probably right but we can leave that out for now.

The formula you would use is:
A = P(1 + r/100)^t

Where A = Amount, P = Principle, R = Interest Rate per annum and t = time in years. But you mentioned you're adding money every month, so the above will give you per annum so the interest will be off by a bit but should be close enough to compute the difference.

The actual formula you would use would depend when interest is computed, so say interest is paid out N times per year then you adjust the formula to this:
A = P[1 + r/(N * 100)]^(Nt)

Where N = number of times per annum interest is paid.

I'll stick to the easy case...

So, Contract A: $2250 * 12 = $27,000 per year
So, Contract B: $2750 * 12 = $33,000 per year

Contract A = $27000*(1.08) ^ 40 = $586,562.08
Contract B = $33000*(1.08) ^ 18 = $131,868.64

Contract A would win.

But remember the numbers are not exact since you can't do $2250 * 12 really since it depends when interest is computed. If interest is computed continiously, that gets even uglier...

Hope this helps Bobble Head :)
WG

I couldn't find a compound interest calculator that would do monthly payments, so I just did yearly... even though these figures will be inaccurate because of that, it's pretty obvious which one is the winner.

A = 7.5m
B = 1.3m

Hmm, my numbers come out very differently to WiredGuy. This is how I entered it:

$0 initial investment
$27,000 or $33,000 per annum additional investment
8% interest calculated and paid annually

Oh wait, if you're adding those amounts each month for the 40 or 18 years then my formula is wrong, I was thinking just the first year.

WG

On A you'd have: $582,877.17

On B you'd have: $102,988.17

Just go on Excel and use this formula on A2: (A1*108%)+2250 and pull it down until 40... A1=2250

On B2 use: (B2*108%)+2750 and do the same thing (pull until 18), with B1=2750

Where do I get my $20??

#b is better by $559,440 if you never touch the money between years 18 and 40.........Maybe........ Now fuckin pay me!!!:stoned

That sure looks close but it doesn't sound right. Why are the numbers so far apart? I'm trying to figure out which contract to choose. Which would you take Wired Guy?

You guys are missing the point. Someone is going to be paying me this monthly payment. I am trying to figure out what the contracts are worth in today's dollars.

The numbers are far apart because of compound interest, you specified an interest rate of 8% and (A) has an extra 22 years to build that up...

This question is a simple NPV calculation.

It can be done in many ways, Excel is probably the quickest & easiest.

You simply enter in the monthly payments for each, the monthly interest rate (8%/12), and the answer pops out for each:

NPV A: $323,595.88
NPV B: $314,299.14

Thus A is $9,296.74 better than B in today's value.

Now how do I pick up my $20? :)

Thanks, but just keep it...

I'm not doing this for money...:Graucho

is the interest compounded annually? monthly @ 8%? or monthly with an 8%/yr average?

or is it compounded daily with a an 8% per year average? :)

Anually

arg, i see numbers and the fact that I have the intelligence of the hulk in the math department becomes so very evident.

I don't understand. I get the monthly interest payment part. But, how did you get the total amount? What is the who formula?

Let me try that again, revised formula:

A = P((1+r)^n-1)/r

Same definitions as I gave before, then we get:

Contract A number of interest periods is n=40
Contract A number of interest periods is n=18

Principle A = 12*2250 = $27000
Principle B = 12*2750 = $33000

Now some math:
Contract A: n = 40, P=27000, R=0.08
27000((1.08)^40 - 1) / 0.08 hahahaha $6,994,526

Contract B: n = 18, P=33000, R=0.08
33000((1.08)^18 - 1) / 0.08 hahahaha $1,235,858

I think that should be correct, contract A wins it still.
WG

Compound Interest Formula:

T = P(1+R)^Y

T = Total
P = Principle
R = Rate
Y = Years

$2,250 per month for 40 years yields a total of $1, 080,000.

40 ( (2250)(12) ) = 1080000.

Have total, solve for principle:

1080000 = var_x ((1 + .08)^40)

$49,713.41 = var_x;

Total initial investment: $49,713.41

----

$2,750 per month for 18 years yields a total of $594,000.

18 ( (2750)(12) ) = 594000;

Have total, solve for principle;

594000 = var_x ((1 + 0.08)^18);

$148,647.97 = var_x;

Total initial investment: $148,647.97

----

That's for compound interest.

Oops.... It's 2,250 and 2,750 a month??? Sorry.... the right formula should be-> montly interest is 1,001203239:

Formula for A. Put 2250 on A1, on A2 write: =(a1*interest)+2250 and pull down until A480!!!

Formula for B. Put 2750 on B1, on B2 write: =(b1*interest)+2750 and pull until B216....

On A you should get: 1460541,37
On B you should get: 677872,51

Now: WHERE IS MY MONEY???

P=A{[1-(1+r)^(-n)]/r}

So the present value of each offer is:
Pa = 2250*{[1-(1+0.08)^(-40)]/0.08} = 26,830.38
Pb= 25,772.68

So you should go for A

Explainning how I got that montly interest rate... Let's call it x...

x^12=1,08
x=1,001203239

Wired Guy and Tranza, your answers are more than the total amount of payments. When I use the calculator located at the lower left corner of this page: http://www.uic.edu/classes/actg/actg500/pfvatutor.htm I get them both coming in around 275,000 dollars. If I am using it right, that is.

Hi Rick check out my answer this is the only answer you should check, and you can take off the $20 from my next wire ;o)

Well NPV (Net Present Value) is simply a formula that puts all future income into present value - as you correctly pointed out, your question revolves around the time value of money.

So what the formula is doing is essentially, for A:

NPV = $2,250/(8%/12) + $2,250/(8%/12)^2 + $2,250/(8%/12)^3 + ...... + $2,250/(8%/12)^480

Does that make sense?

Is it possible that your answer is correct yet only off by a decimal point?

I'm just computing the calculations based on my acturial sciences courses I did. But look at it this way:

$2250 * 12 months * 40 years = $1,080,000
$2750 * 12 months * 18 years = $594,000

No interest in the above calculated and contract A is worth almost twice as much. Now factor that contract A is compounding interest for twice as long and it makes sense to me that Contract A is much more valuable and by a factor of 3-4 times. Seems to make sense to me.

WG

nop, it is the present value, if you want to know the value in the end of the period you need to use a deferent Formula, but it doesn't mater any way, because you need to know what is the best offer, and the best way to check it out is by using the present value of the offer.

there is no logic in checking what will be the value of a in another 40 years and to comper it to the value of b in another 18 years.

You need to bring bouth offers to the same date, and that is why you are useing the present value formula.

you can trust me, I have an MBA from Wharton

I would have thought the opposite. But you are a good businessman. You are saying that you would take contract A even though you'd get 6,000 dollars a year less over 18 years?

this is a funny thread :1orglaugh

Uhm.... Impossible....

Disconsider the interest: 2250 * 12 * 40 = 1,080,000
2750 * 12 * 18 = 594,000