I get weird numbers. Can you provide an Open Document Spreadsheet with an example?
I did the calculation with some real numbers and included the output of an excel spreadsheet.
P: original loan amount (i.e. $10000)
d: deflation rate (i.e. 3%)
D = 1-d (i.e. 0.97)
i: loan interest rate (i.e. 5%)
I = 1+i (i.e. 1.05)
n: term length of loan (i.e. 10)
k: current pay period payment is being calculated for
Here is a general formula for the k'th payment amount.
payment[k] = P*I*(1-D/I)/(1-(D/I)^n)*D^(k-1)
Here is the first payment using the numbers:
Payment[1] = 10500*(1-0.97/1.05)/(1-(0.97/1.05)^10) = $1,461.76
Here is what it looks like in excel.
Note: Outstanding is 1.05 times the remaining principle. The Payment is per the formula above, and the Remain is the Outstanding minus the Payment.
k Outstanding Payment Remain
1 $10,500.00 $1,461.76 $9,038.24
2 $9,490.15 $1,417.91 $8,072.25
3 $8,475.86 $1,375.37 $7,100.49
4 $7,455.51 $1,334.11 $6,121.40
5 $6,427.47 $1,294.09 $5,133.39
6 $5,390.06 $1,255.26 $4,134.79
7 $4,341.53 $1,217.60 $3,123.93
8 $3,280.13 $1,181.08 $2,099.05
9 $2,204.00 $1,145.64 $1,058.36
10 $1,111.28 $1,111.28 $0.00
As required, each payment is 3% less than the previous payment and the balance is paid in full.
I found the following URL helpful in understanding the formulas:
http://www.mathpages.com/home/kmath297.htm(Note: In the mathpages' URL they talk about inflation instead of deflation so their "I" is my "D" and my "I" is their "Y". I just picked "I" and "D" to correspond to the "i" and "d" already being used in this thread.)