The Economic Consequences of Homelessness in The US

m = payment amount
n = amount payment periods
LN = natural logarithm
For Finding Remaining Principal Balance
The following formula will calculate your remaining balance if you have made t of N
fixed payments in a timely basis (i.e. by the due date) so that no additional interest has
accrued.
where:
P = P*(1 -((1 + J)**t - 1)/((1 + J)**N - 1))
P = principal, the initial amount of the loan
I = the annual interest rate (from 1 to 100 percent)
L = length, the length (in years) of the loan, or at least the length over which the
loan is amortized.
J = monthly interest in decimal form = I / (12 x 100)
N = number of months over which loan is amortized = L x 12
t=number of paid monthly loan payments
This is from Mortgage Backed Securities by William W Barlett and was sent to me by
Victor Kheyfets.
If you would like to calculate an outstanding loan balance but have not made regular
fixed payments by the due date, you will have to fill out an accurate payment schedule
within a spreadsheet, or similar application where you can account for missing and
different payments.
Finding the Interest Rate Given Loan Amount, Payment and Number
of Periods
Many folks have asked me for a simple formula to calculate the interest rate give the
other three terms (loan amount, payment and # of periods). I can calculate the number
easily enough, but I have no idea if there is a simple formula to do it or not. I do it the
good old fashioned way -- plug and chug! Luckily, a computer program makes "plug and
chug" trivial and speedy with a simple binary search:
min_rate = 0; max_rate = 100; # Set Maximum and minimum rate
while (min_rate < max_rate - 0.0001)
{
mid_rate = (min_rate + max_rate) / 2; # Divide by 2
J = mid_rate / 1200; # Convert to monthly decimal
# calculate payment from interest, term and loan_amt
guessed_pmt = loan_amt * ( J / (1 - (1 + J) ** -N ));
Page 234 of 289