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Do we PM you the answer? I think I can do this off the top of my head.

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Nah, Just post the whole thing here.

Initial amounts, Problem, Solution and Answer.

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I wish the world was flat like the old days
Then i could travel just by folding a map
No more airplanes, or speedtrains, or freeways
There'd be no distance that can hold us back.

You mean like a bond value problem?
This takes considerable time to write a full report on, it's unlikely that people will do this kind of work for free. (sorry, points =! rewards:P )

But i'll make up a problem for ya though:P That part is usually the hardest anyways:P

Today, you take out a 10,000,000$ (10 million dollar) loan at QR of 8.5%, under the agreement that unpaid interest is simply rolled into the principal amount. In one month you pay a first payment of 1$, on the second month you pay a payment of 2$, on the third month you pay a payment of 4$, etc. etc. doubling the previous months payment until the loan is paid off.

On the last payment of the loan a certain amount of money is left over (as you overpay using this scheme). You take that amount and invest it in an annuity at the same QR (8.5%) as the loan, and the annuity pays out 1$ the first month, 1.50$ the second month, 2.25$ the third month, etc. etc. making 1.5x the payment of the prvious month until the loan is paid off (the last month you simply pay out the money that is left in the annuity).

What is the Present Value (PV) of this annuity discounted back to today at 7% EAR?

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present value problem?  

You mean like a bond value problem?  
This takes considerable time to write a full report on, it's unlikely that people will do this kind of work for free. (sorry, points =! rewards:P )

But i'll make up a problem for ya though:P That part is usually the hardest anyways:P  

Today, you take out a 10,000,000$ (10 million dollar) loan at QR of 8.5%, under the agreement that unpaid interest is simply rolled into the principal amount. In one month you pay a first payment of 1$, on the second month you pay a payment of 2$, on the third month you pay a payment of 4$, etc. etc. doubling the previous months payment until the loan is paid off.

On the last payment of the loan a certain amount of money is left over (as you overpay using this scheme). You take that amount and invest it in an annuity at the same QR (8.5%) as the loan, and the annuity pays out 1$ the first month, 1.50$ the second month, 2.25$ the third month, etc. etc. making 1.5x the payment of the prvious month until the loan is paid off (the last month you simply pay out the money that is left in the annuity).

 
What is the Present Value (PV) of this annuity discounted back to today at 7% EAR?

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What? That's too complicated for me.

I do them like this:

Alli will Owe $3589 on a loan calculated at 12% per year , compounded monthly, in 2 years. How much is he being charged?

See, less words = better!

But thanks. I just can't use that one or they'll think I suddenly got a brain or something.  

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I wish the world was flat like the old days
Then i could travel just by folding a map
No more airplanes, or speedtrains, or freeways
There'd be no distance that can hold us back.

Maybe you should set up some sort of payment plan, it'll be easier to set up the excel this way;)

So let's use this payment method:
You start off paying $1, then next you pay $2, etc.

Then on Excel
A1 you put in $3589
B1 you put in A1*1.01
From C2 --> C(anything) go 0,1,2,3...
Then A2 you put in A1 - 2^C2

Then let D1 = B1-A1

Now drag down A, B, C and D columns.
When A reaches <0. You Sum the D values, that's the amount of interest this guy have paid, and that would be the value on that loan (If you are to sell it).

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is the 12% the annual interest rate?  

Maybe you should set up some sort of payment plan, it'll be easier to set up the excel this way;)

So let's use this payment method:  
You start off paying $1, then next you pay $2, etc.

Then on Excel
 A1 you put in $3589
B1 you put in A1*1.01
From C2 --> C(anything) go 0,1,2,3...  
Then A2 you put in A1 - 2^C2

Then let D1 = B1-A1

Now drag down A, B, C and D columns.  
When A reaches <0. You Sum the D values, that's the amount of interest this guy have paid, and that would be the value on that loan (If you are to sell it).

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See you are confusing the hell out of me. I'm not used to do it like that. =/

I can't even solve that problem D= I think it makes sense, That's the Spread and Sheet method, right? Is that with Excel? I can't do it on Excel I don't get it. =/

How would you solve that if you had to do it with a Graphing Calculator or a Scientific Calculator? - Those are the methods I know how to use - But so far I can't make it. I don't know! I lack of certain quantities to be able to solve it.. And your explanation though makes sense seems like the most confusing thing ever. haha

To make it on a scientific calculator I need to have the principal of the loan (P) which I don't have!, A = 3589 (the amount of the loan in 2 years.)
n = 2 x 12 ( 2 years monthly interest periods)
i= 12% = O.012?  ugh

and put it in these formula: A = P (1+i)^n

3589 = P (1 + 0.12) ^ 24
3589 = P (1 .12) ^ 24

Then I have to set up a chart with i and A and guess the different values of i and check weather the value of A equals 3589.

Something like that. Aghhh my head!

-------
I wish the world was flat like the old days
Then i could travel just by folding a map
No more airplanes, or speedtrains, or freeways
There'd be no distance that can hold us back.

Why don't you set it up like this:
Annual Interest rate = 12% compounded monthly, so that's 1% per monthy. (APY will be slightly above 12% with this)

I'd think Excel is much easier because it saves you a LOT of calculations. If you are going to do finance, you need to learn Excel very well. (I interned for finance departments for 1.5 years)

For your chart: I suggest the following method:
Why don't use a fixed payment method to make it slightly easier (say $100 a month fixed? )

First Column: Time (start with t=0)
Second column: Money owned
Third Column: Interest added to Second column AFTER payment
Forth Column: Have the third column subtract the second column.

So say you loan $1000

0 $1000 $1010 $10
1  $910  $919.1 $9.1
etc.

When Column 2 goes <0, you add up the forth column for the value of the loan.

Calculating the EXACT amount you must pay each month to end the loan in a specific date is kinda complicated and should be avoided if possible:P

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Well, I think putting a fixed time period would make this problem harder, it's easier if you just come up with a plan;)  

Why don't you set it up like this:
Annual Interest rate = 12% compounded monthly, so that's 1% per monthy. (APY will be slightly above 12% with this)

I'd think Excel is much easier because it saves you a LOT of calculations. If you are going to do finance, you need to learn Excel very well. (I interned for finance departments for 1.5 years)

 
For your chart: I suggest the following method:
Why don't use a fixed payment method to make it slightly easier (say $100 a month fixed? )

First Column: Time (start with t=0)
Second column: Money owned
Third Column: Interest added to Second column AFTER payment
Forth Column: Have the third column subtract the second column.  

So say you loan $1000

0 $1000 $1010 $10
1 $910 $919.1 $9.1
etc.

When Column 2 goes <0, you add up the forth column for the value of the loan.  

Calculating the EXACT amount you must pay each month to end the loan in a specific date is kinda complicated and should be avoided if possible:P

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But that's a problem I have to resolve. I can't change it.   They gave me that I can't go changing the numbers. D=

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I wish the world was flat like the old days
Then i could travel just by folding a map
No more airplanes, or speedtrains, or freeways
There'd be no distance that can hold us back.

Let x be the amount that the guy pays every month so that he pays up after 24 months.

I'm assuming 12% is the annual interest rate (sorry, 12% per month seems ridiculously high:P ), so that's 1% per month.

Let's set it up like this, going from t=0 to t=24

0 $3589                  $3589*1.01
1 $3589*1.01 -x      ($3589*1.01 -x )*1.01

...

at t=24
You'll have (($3589*1.01 -x)*1.01-x)...
do that recursion 24 times. and that have to =0

So now you have a recursion formula:
with t1 = $3589*1.01 -x
and t2 = (t1*1.01)-x

you need a specific x so that t24=0
You'll need to set up matrices and solve for the engenvalues of this recursion sequence.
With that, you should be able to solve for the correct x after a ton of grinding.

Seriously, this doesn't look that plausible by hand. I suggest using MATLAB or similar programs to solve for the engenvalues and x.

Once you gotten x, then use that format I showed you earlier to solve for the value of your loan.

t24=(t23*1.01)-x = 0
x = t23*1.01

Then plug in t23=(t22*1.01)-x

and keep going until you get to t0, which is also a known value:P

What do the T mean? =/

:( This is like German for me. D= I don't get it.

And the interest is 12% high or not .. That's what they tell me. I just want to know how much interest rate they are charging him! D=

What I think that you are too advanced for me. I just need basics and answers. D=

Post edited at 12:29 am on Aug. 27, 2008 by iJeannie

-------
I wish the world was flat like the old days
Then i could travel just by folding a map
No more airplanes, or speedtrains, or freeways
There'd be no distance that can hold us back.