Outstanding Loan Balance - Prospective Method¶

Another way to calculate the outstanding loan balance at a point in time is the prospective method, which sums up the value of the remaining loan payments, discounted to that time period. Assuming compound interest, if the last payment is adjusted to avoid over/under payment, the outstanding loan balance calculated via the prospective method is defined as:

$\text{OLB}_k = Q\ax{\angl{n-k-1} i} + R(1 + i)^{-(n-k)}.$

If all the payments are equal, it is defined as:

$\text{OLB}_k = Q\ax{\angl{n-k} i}.$

The advantage of the prospective method is that we do not need to know the original loan amount.

Examples¶

Suppose we need to make 10 end-of-year payments of 5,000 to pay off a loan. Assuming the rate of interest is 5% compounded annually, what is the outstanding loan balance immediately after the 5th payment?

We can solve this by using TmVal’s Loan class. First, we define the loan by providing the characteristics in the preceding paragraph. Then, we call the method Loan.olb_p() to execute the prospective method:

In [1]: from tmval import Loan, Rate

In [2]: my_loan = Loan(
   ...:    pmt=5000,
   ...:    gr=Rate(.05),
   ...:    period=1,
   ...:    term=10
   ...: )
   ...: 

In [3]: print(my_loan.olb_p(t=5))
21647.383353154095

Now, suppose we miss the 4th and 5th payment. What is the outstanding loan balance at time 5?

We can solve this by again calling the Loan.olb_p(), and supplying the 4th and 5th payments as a list to the missing argument, missing=[4, 5]:

In [4]: print(my_loan.olb_p(t=5, missed=[4, 5]))
31897.383353154095