Outstanding Loan Balance - Retrospective Method¶

A common problem involving loans is calculating the outstanding loan balance at a point in time. One way to do this is called the retrospective method, which first calculates the accumulated value of the principal, and then subtracts the accumulated value of the payments. The formula for the outstanding loan balance after the $k\text{-th}$ payment is thus:

$\text{OLB}_k = La(k) - Q\sx{\angl{k}}$

The main advantage of the retrospective method is that we do not need to know the term or the total number of payments required to settle the loan.

Examples¶

Suppose we have borrowed 50,000 to be paid off with annual end-of-year payments of 5,000. If the interest rate is 5% compounded annually, what is the outstanding loan balance immediately after the 5th payment?

We can solve this problem with TmVal’s Loan class, which is its main class for performing loan calculations. First, we need to define the loan by setting the arguments for the loan amount, amt=5000, the payment amount, pmt=5000, the payment period, period=1, and the interest rate.

We can call the method Loan.olb_r() to apply the retrospective method to find the balance at time t=5:

In [1]: from tmval import Loan, Rate

In [2]: my_loan = Loan(
   ...:    amt=50000,
   ...:    pmt=5000,
   ...:    period=1,
   ...:    gr=Rate(.05),
   ...: )
   ...: 

In [3]: print(my_loan.olb_r(t=5))
36185.921875