Financial calculation

Terry fastsnip-bcard1 at
Fri Jan 7 13:45:43 EST 2005

On Friday 07 January 2005 04:47, saher edris wrote:
> Suppose i'm processing the following lease transaction with the following
> input parameters :
> lease created date = Sep., 13 th 2004
> first payment date  = Nov., 30 th 2004
> * grace period is considered " accounted for " since lease creation date up
> to first payment date .
> p.v. " lease amount " =  6725 $
> no. of payments        = 72   months
> payment amount    = 118
> f.v.  "lease amount + interest" = 10436 $
> balloon amout = 1440
> no. of balloon payments = 6
> balloon payment = 240
> balloon first payment date = Oct.,30 th 2005
> CF = PF = monthly
> My question is .... in trying to find the value of  the " nominal rate " 
> ...does the existance of
> balloon payments affect the calculation of the " nominal rate "  ? and if
> it does please explain ?

Your numbers translate into the following parameters:

Present Value == pv = 6725

number of periods == n = 72 (months  == 6 years)

periodic payment == pmt = -118 (note that minus sign, since (I assume) this 
money is being paid out, then it is negative. If you neglect the minus sign, 
and try to compute an interest, you will get a calculation that never ends, 
i.e., it will oscillate between positive and negative values (and rather 
large values) for the interest rate. The calculation will never converge on a 
value. It cannot converge, since with a positive 'pmt' value you will have an 
'insoluble' problem - i.e., no solution.)

After this your scenario departs radically from the scenario that can be 
handled by the financial calculations I submitted to gnucash. You posit 6 
"balloon" payments of -240 (again negative) starting approximately 12 months 
(1 year) after the initial payment. This is in addition to the periodic 
payments made during the 6 years of the life of the transaction. 

There is no way to account for your "balloon" payments in the computations as 
I submitted them to gnucash. 

Now "balloon" payments as that term is "normally" handled by financial 
institutions (at least in the US) means a single payment made at the end or 
termination of the entire transaction, i.e, on the final payment and not 
during the life of the transaction.  

Thus,  a "balloon" payment as used by US financial institutions (and I am 
pretty sure as used world wide by financial institutions) would be a single 
payment of 1440 as the 73rd payment.

Thus, added to the above parameters you would have:

Future Value == fv = -1440.

With this value you now have four parameters (besides CF, PF, discrete or 
continous, and beginning or end of period payments - assuming the typical 
values for those). You can now solve for an interest rate. Making this 
computation you have:

pv = 6725
n = 72
pmt = -118
fv = -1440

solving: i = 12.0702 Nominal Annual Interest Rate or 
    Effective Interest Rate Per Payment Period: 0.0101092

How you are going to handle your 6 "balloon" payments during the life of the 
transaction is anybody's guess. Those payments cannot be handled by the 
financial calculations as I submitted to gnucash.

You could possibly break the transaction into 6 separate transactions, each of 
12 months duration, each with monthly payments of 118, each transaction 
starting on the payment of the previous transaction's "balloon" payment and 
with a pv equal to the balance remaining on the previous transaction.

Setting up the transaction in this fashion, you would compute a nominal 
interest rate for the 6 year period of:

i = 8.02708 

At the end of the first 12 month period, the future value would be:

fv = -5,815.86

Using this (less 240) as the basis for the next 12 months we would have the 

pv = 5,815.86 - 240 = 5,575.86
pmt = -118
i = 8.02708 

Using these compute a Future Value at the end of the second 12 months as:

fv = -4,571.00

For the 3rd 12 month period, we would have:

pv = 4,571.00 - 240 = 4,331.00
pmt = -118
i = 8.02708

Which leaves a Future Value at the end of the 3rd 12 months of:

fv = -3,222.46

For the 4th 12 month months we have:

pv = 3,222.46 - 240 = 2,982.46

which leaves a Future Value at the end of the 4th 12 month period of:

fv = -1,761.60

For the 5th 12 month period we have:

pv = 1,761.60 - 240 = 1,521.60

which leaves a Future Vaule at the end of the 72 periodic payments of:

fv = -179.06

and thus a Final "balloon" payment of 179.06. 

Note that the last "balloon" payment is not 240 exactly since the previous 
payments of 240 have reduced the principle upon which the interest is 

Your scenario with 6 payments of 240 during the life of the transaction would 
have to have a different interest rate than what I have computed since the 6 
payments reduce the principle during the 6 years of the transaction.

> P.S. this is an actual transaction with actual parameters

This may be an "actual" (maybe even typical) leasing transaction (you keep 
writing about "lease amount" and "lease transaction", etc), but it is NOT an 
actual or typical transaction for a financial institution in loan or interest 
generating transactions.

If any gnucash user or developer can supply data or details on any financial 
institution that would consider such a transaction as typical, I would be 
most happy to learn of such transactions. If they could be explained lucidly 
and in detail, maybe a means of computing such transactions could be worked 

Hope this helps,

> Regards
> Saher Edris
> ---------------------------------
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