compound in a Peer 2 peer loan program

[Agomes]

Hello guys,

I am not a Math wizard and actually am looking for a formula/equation to calculate roughly the example below.

I have signed myself into a loan lending program where i can give you an example:

I invest 20,000 euros in multiple loans at a 15% annual rate with 48 months of payment schedule.

Actually every month when the money enters my account I end up reinvesting 100 % in new loans (same interest rate 15% with the same 48 months) - the initial money + interest rate of 15 %

Let's assume for all logical proposes that i do not end up having bad loans situations so 100 % of the money loaned returns to me (ps: i know it's impossible )

Also that the money arrives always at the same percentage (1/48 of the initial amount each month plus the interest rate) - i know that actually this is not true, but for this exercise i do not need to find out how this program is actually dividing the interest rate/initial invest amount in the return parcels.

I want to build a theorical model and afterwards i can start thinking of a more real one as i get the percentage of no-returns or bad loans into the equation.

This process is to last for example 4 years / 8 years / 12 years.

Please feel free to ask me anything as I may not ended up explained correctly something.

Best

Antonio

 

[Ishuda]

Hello guys,

I am not a Math wizard and actually am looking for a formula/equation to calculate roughly the example below.

I have signed myself into a loan lending program where i can give you an example:

I invest 20,000 euros in multiple loans at a 15% annual rate with 48 months of payment schedule.

Actually every month when the money enters my account I end up reinvesting 100 % in new loans (same interest rate 15% with the same 48 months) - the initial money + interest rate of 15 %

Let's assume for all logical proposes that i do not end up having bad loans situations so 100 % of the money loaned returns to me (ps: i know it's impossible )

Also that the money arrives always at the same percentage (1/48 of the initial amount each month plus the interest rate) - i know that actually this is not true, but for this exercise i do not need to find out how this program is actually dividing the interest rate/initial invest amount in the return parcels.

I want to build a theorical model and afterwards i can start thinking of a more real one as i get the percentage of no-returns or bad loans into the equation.

This process is to last for example 4 years / 8 years / 12 years.

Please feel free to ask me anything as I may not ended up explained correctly something.

Best

Antonio

The initial model you want is just the simple compound interest model. That is if you are going to reinvest everything and have no defaults, that is the same as not taking any payments and letting it grow. So the effect is just getting the interest for the first period, then the interest and interest on the interest for the second, then the ... which is just compound interest or the future value (FV) formula
FV = PV (1+i)ⁿ
where PV is the present value (the €20,000), i is the interest rate per period (0.15/12 in your case) and n is the number of periods (48 in your case).

The easiest way to account for default may be to just adjust the interest rate. For example, you invest $48,000 at 15% (1.25% per month) for 48 months at a 2% default rate. So, you are supposed to get $1000 in return of capital (which you will re-invest) and $600 in interest for a total of $1600. However at a default rate of 2%, you only get $1568 [an actual loss of $20 in capital return and $12 in interest]. Taking out the $1000 for reinvestment of capital leaves a return of $568 or an effective interest rate of 14.2%

 

[Ishuda]

MONTH  TRANSACTION   INTEREST    BALANCE
  0      20,000             0     20,000
  1        -557           250     19,693 [1]
  1         557             0     20,250 [2]
  2        -564           253     19,939
  2         564             0     20,503
...and so on

[1]: 20000 * .15 / 12 = 250
[2]: payment reinvested
I've rounded out calculations (closest dollar...or euro!)
The 557 is the montly payment on the initial 20,000 loan,
for 48 months.

"Globally", is that "what d'heck's going on"?

'Twas about what I though. Since the -557/+557 (and -564/+564 ...) is a wash it doesn't make any difference what it is but I though the amount was just a 'return of 1/periods part of capital'

EDIT: That payment of $557 looks like the standard payment on an 'installment loan' which would partially include a return of principle [capital in this case] and also the (initial) $250 interest so I don't think that is exactly what was meant but the idea is there.

 

[Ishuda]

Does not matter what the interest amount is;
only the CASH is reinvested, which is the payment...

MONTH  TRANSACTION   INTEREST    BALANCE
  0      20,000             0     20,000
  1        -557           250     19,693 [1]
  1         557             0     20,250 [2]
  2        -564           253     19,939
  2         564             0     20,503
...and so on

...

Rounded
20000*(1.0125)¹=20250
20000*(1.0125)²=20503
20000*(1.0125)³=20759
etc.
So your comps are the same as the FV formula above
...

 

[Agomes]

Thanks guys. This was helpful

Actually what happens in the "real model " is this:

Period " 0 " (or "in the beginning"), all the 20,000 euro gets an investment, so that the balance in the end of that period is 0. Then, in the second month, you have the return of 1/48 + interest rate which is automatically re-invested. So the model explained here:

MONTH	TRANSACTION	INTEREST	BALANCE
0	20,000	0	20,000
1	-557	250	19,693 [1]
1	557	0	20,250 [2]
2	-564	253	19,939
2	564	0	20,503

...and so on

doesn't seem to take that in account.

 

[stapel]

...in the second month, you have the return of 1/48 + interest rate

What do you mean by "plus interest rate". Does this mean "plus the interest which had been paid to the account"?

So the model explained here:

...and so on

doesn't seem to take that in account.

What do you mean by "in account"? Are you saying that some account transaction which you think should have taken place did not take place? Or are you saying that something (perhaps in the table) does not take something "in to account", meaning that some consideration of the original exercise is not reflected in the posted computational results? If the latter, then hat doesn't take which into account?

Please be complete. Thank you!

 

[Ishuda]

Thanks guys. This was helpful

Actually what happens in the "real model " is this:

Period " 0 " (or "in the beginning"), all the 20,000 euro gets an investment, so that the balance in the end of that period is 0. Then, in the second month, you have the return of 1/48 + interest rate which is automatically re-invested. So the model explained here:

MONTH	TRANSACTION	INTEREST	BALANCE
0	20,000	0	20,000
1	-557	250	19,693 [1]
1	557	0	20,250 [2]
2	-564	253	19,939
2	564	0	20,503

...and so on

doesn't seem to take that in account.

Just change the -557/+557, etc to -416.67/+416.67 [1/48th part of the 20,000] and I believe you have what you want. The - part of the transaction would be the 1/48th part being returned to you and the + part would be the reinvestment.