Loan_Payment_Optimizer

Descripton:

Python code to determine how to allocate extra money to minimize the total cost paid on debt in the form of amortized loans.

Brief explanation:

Let's say you have a bunch of debts. They are probably in the form of loans paid off in installments over time. These are known as amortized loans.

Examples of amortized loans include student loans, mortgages, and credit card debts.

The mantra I've seen over and over again, is that the optimal way to pay off these debts is something called the "higher rate" or "descending interest" method by which you pay off your debts by interest rate from highest to lowest [1][2].

I wanted to test to see if the descending interest method was always optimal. To test this hypothesis, I coded up a simple algorithm I call the "gradient descent" method which I thought might be a worthy competitor. It operates on a set of loans by seeing which loan's total cost (the interest + principal you pay over life of the loan) is reduced the most by applying a fixed amount of money over the fixed minimum payment. You can read more about the function in its comments within the loan_function.py file.

I hypothesized that the "gradient descent" method would result in a lower total cost paid in at least some scenarios, compared to the "descending interest" method.

I put the hypothesis to the test in two separate ways:
1 - By running a bunch of debt scenarios through each of the algorithms.
2 - By a simple total cost plot made varying only one loan parameter for a two-loan scenario.

The bottom line is the descending interest method is not always optimal, although I do think it's a good rule of thumb.

To see the results of 1, see README.md in the loan_function_test_1_in4 sub-directory.

The results of 2 are shown below. Please look at the simple code method_compare_1.py to see how I made these plots.

The figure above shows how the gradient descent method reduces the total cost paid over the life of two loans assuming the following...

1. The annual interest of Loan A is 35%.
2. The annual interest of Loan B is 10%.
3. The term of both loans is 100 months.
4. The TOTAL amount of money applied above the minimum payments is $100. The way this $100 is split between Loans A & B is what is determined by the gradient descent algorithm. The descending interest algorithm ALWAYS applies the $100 to the loan with the higher interest rate until it's paid off.
5. The starting principal of Loan A is $500.
6. The starting principal of Loan B varies. It varies from being equal to Loan A's starting principal to + $10000 greater.

The top plot in the figure compares the total cost of the two methods as a function of the increases in Loan B's starting principal. The bottom plot explicitly shows how much money you would save using the same x-axis.

Granted, I picked a case where I knew the gradient descent method would win. But the point is that the descending interest method is not always optimal if you are trying to reduce your total cost paid.

If you look at the results of 1, the many debt scenarios, you'll see that the majority of the time the gradient descent outperforms the descending interest method, and in cases where it does not, it doesn't "lose" by much.

System requirements:

• Python 3.X
• No obscure Python libraries required.

References:

[1] https://www.khanacademy.org/college-careers-more/personal-finance/pf-interest-and-debt/debt-repayment/v/high-rate-vs-snowball-method
[2] https://www.reddit.com/r/personalfinance/comments/zzoxu/calculator_to_optimize_loan_payoff/ {last accessed 9/9/20}

Notes:

{17 Aug 2020}
First draft complete.

{09 Sep 2020}
Considering the time value of money is beyond the scope of this project. For example, it could sometimes be better to put some extra money towards high-return investments rather than paying off some debts.