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Old 07-02-2003, 05:32 PM   #1
Rick Latona
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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.
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Old 07-02-2003, 05:34 PM   #2
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One of your advertisers wants to pay for a banner 40 years up front to get a better deal?
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Old 07-02-2003, 05:35 PM   #3
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i'll take B
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Old 07-02-2003, 05:35 PM   #4
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damn. I'm so bad at math.
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Old 07-02-2003, 05:35 PM   #5
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compound interest?
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Old 07-02-2003, 05:36 PM   #6
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Is this a test?


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Old 07-02-2003, 05:36 PM   #7
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The Answer is A

the formula is im too lazy to do it and i have a 50/50 chance
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Old 07-02-2003, 05:36 PM   #8
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b
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Old 07-02-2003, 05:37 PM   #9
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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.
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Old 07-02-2003, 05:37 PM   #10
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damn, I dont understand the question, but I know how to solve if I understood it 100%
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Old 07-02-2003, 05:37 PM   #11
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Quote:
Originally posted by Mr.Fiction
One of your advertisers wants to pay for a banner 40 years up front to get a better deal?
LOL I wish.
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Old 07-02-2003, 05:37 PM   #12
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I could tell you B is worth half as less as A
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Old 07-02-2003, 05:38 PM   #13
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LOL I wish.
without interest A is over 1 Mil, and b is 550,000
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Old 07-02-2003, 05:38 PM   #14
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Quote:
Originally posted by bdjuf
damn, I dont understand the question, but I know how to solve if I understood it 100%
Someone needs to reverse the compound interest. What don't you understand?
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Old 07-02-2003, 05:39 PM   #15
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Quote:
Originally posted by JDog


without interest A is over 1 Mil, and b is 550,000
No shit, Sherlock.
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Old 07-02-2003, 05:40 PM   #16
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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?"; }

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Old 07-02-2003, 05:41 PM   #17
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In order to figure the time value of money you need a number to use for inflation right?
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Old 07-02-2003, 05:41 PM   #18
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Quote:
Originally posted by Arty
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 { "Do you want that money for your grand sons to spend"; }

I like that!
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Old 07-02-2003, 05:42 PM   #19
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Quote:
Originally posted by Arty
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 { "Do you want that money for your grand sons to spend"; }

Dude, I might just send you 20 dollars anyway.
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Old 07-02-2003, 05:43 PM   #20
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Quote:
Originally posted by Lenny2
In order to figure the time value of money you need a number to use for inflation right?
In a perfect world you are probably right but we can leave that out for now.
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Old 07-02-2003, 05:43 PM   #21
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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
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Old 07-02-2003, 05:43 PM   #22
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Quote:
Originally posted by Rick Latona
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.
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
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Old 07-02-2003, 05:46 PM   #23
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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
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Old 07-02-2003, 05:46 PM   #24
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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.

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Old 07-02-2003, 05:47 PM   #25
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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??
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Old 07-02-2003, 05:48 PM   #26
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#b is better by $559,440 if you never touch the money between years 18 and 40.........Maybe........ Now fuckin pay me!!!
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Old 07-02-2003, 05:48 PM   #27
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Quote:
Originally posted by WiredGuy
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
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?
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Old 07-02-2003, 05:50 PM   #28
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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.
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Old 07-02-2003, 05:50 PM   #29
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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?
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...
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Old 07-02-2003, 05:50 PM   #30
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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?
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Old 07-02-2003, 05:50 PM   #31
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Dude, I might just send you 20 dollars anyway.
Thanks, but just keep it...

I'm not doing this for money...
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Old 07-02-2003, 05:51 PM   #32
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is the interest compounded annually? monthly @ 8%? or monthly with an 8%/yr average?
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Old 07-02-2003, 05:52 PM   #33
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or is it compounded daily with a an 8% per year average?
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Old 07-02-2003, 05:52 PM   #34
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Quote:
Originally posted by KC
is the interest compounded annually? monthly @ 8%? or monthly with an 8%/yr average?
Anually
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Old 07-02-2003, 05:55 PM   #35
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arg, i see numbers and the fact that I have the intelligence of the hulk in the math department becomes so very evident.
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Old 07-02-2003, 05:55 PM   #36
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Quote:
Originally posted by BlueDesignStudios
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?
I don't understand. I get the monthly interest payment part. But, how did you get the total amount? What is the who formula?
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Old 07-02-2003, 05:56 PM   #37
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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.
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Old 07-02-2003, 05:57 PM   #38
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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.
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Old 07-02-2003, 05:58 PM   #39
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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???
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Old 07-02-2003, 05:59 PM   #40
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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
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Old 07-02-2003, 06:00 PM   #41
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Explainning how I got that montly interest rate... Let's call it x...

x^12=1,08
x=1,001203239
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Old 07-02-2003, 06:01 PM   #42
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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.
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Old 07-02-2003, 06:03 PM   #43
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Quote:
Originally posted by Rick Latona
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)
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Old 07-02-2003, 06:04 PM   #44
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Quote:
Originally posted by Rick Latona


I don't understand. I get the monthly interest payment part. But, how did you get the total amount? What is the who formula?
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?
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Old 07-02-2003, 06:05 PM   #45
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Originally posted by traffic addict


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)
Is it possible that your answer is correct yet only off by a decimal point?
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Old 07-02-2003, 06:07 PM   #46
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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
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Old 07-02-2003, 06:09 PM   #47
traffic addict
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Quote:
Originally posted by Rick Latona


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

Last edited by traffic addict; 07-02-2003 at 06:16 PM..
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Old 07-02-2003, 06:11 PM   #48
Rick Latona
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Quote:
Originally posted by WiredGuy
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
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?
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Old 07-02-2003, 06:11 PM   #49
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this is a funny thread
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Old 07-02-2003, 06:12 PM   #50
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Quote:
Originally posted by Rick Latona
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.
Uhm.... Impossible....

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