Home

Simple Walkthrough with 0 APRs

Consider the following (unrealistic but easy to follow) configuration

{
	"budget": 30,
	"cards": [{
		"cardNickName": "Card1",
		"cardApr": 0,
		"cardBalance": 51,
		"minPayment": 10,
		"maxPayment": 51,
		"actualPayments": 10
	},
	{
		"cardNickName": "Card2",
		"cardApr": 0,
		"cardBalance": 100,
		"minPayment": 10,
		"maxPayment": 100,
		"actualPayments": 10
	},
	{
		"cardNickName": "Card3",
		"cardApr": 0,
		"cardBalance": 51,
		"minPayment": 10,
		"maxPayment": 51,
		"actualPayments": 10
	}
	]
}

It's easy to see that there will never be any accrued interest and as such, any payment plan that fully uses the budget should be optimal.

• Allocation API

balance 1	balance 2	balance 3	Month
51	100	51	1

The data always begins with the current balance. The question is then:

How should I split my $30.00 budget on these 3 cards so that the total balance with accrued interest 
(this time next month) is lower than what it would be if I only made the minimum payments?

Well for the minimum payment of $10 the next balance should be (balance - 10) * (1 + 0 / 12) since the APR is 0 for each card. Unsurprisingly the optimal suggested payment allocation is also $10.00 for each card!

Send a post request to the the API with the json content above. The result should be

{
    "budget": 30,
    "solution": "Optimal",
    "initialBalance": 202,
    "endBalanceOnMinimumPayment": 172,
    "endBalanceOnCurrentPayment": 172,
    "endBalanceOnSuggestedPayment": 172,
    "updatedCards": [
        {
            "cardNickName": "Card1",
            "cardBalance": 51,
            "cardApr": 0,
            "minPayment": 10,
            "maxPayment": 51,
            "actualPayments": 10,
            "suggestedPayment": 10,
            "nextBalanceOnSuggested": 41,
            "nextBalanceOnMin": 41,
            "nextBalanceOnCurrentPayment": 41
        },
        {
            "cardNickName": "Card2",
            "cardBalance": 100,
            "cardApr": 0,
            "minPayment": 10,
            "maxPayment": 100,
            "actualPayments": 10,
            "suggestedPayment": 10,
            "nextBalanceOnSuggested": 90,
            "nextBalanceOnMin": 90,
            "nextBalanceOnCurrentPayment": 90
        },
        {
            "cardNickName": "Card3",
            "cardBalance": 51,
            "cardApr": 0,
            "minPayment": 10,
            "maxPayment": 51,
            "actualPayments": 10,
            "suggestedPayment": 10,
            "nextBalanceOnSuggested": 41,
            "nextBalanceOnMin": 41,
            "nextBalanceOnCurrentPayment": 41
        }
    ]
}

But what's more interesting is to look at the next 12 months of this process.

• Progress API

Use this API and inspect the output.

Assume you are making minimum payments (or suggested payments for that matter)

balance 1	balance 2	balance 3	Month
51	100	51	1
41	90	41	2
31	80	31	3
21	70	21	4
11	60	11	5
1	50	1	6

Well at this point, payments of $1 are required for Card1 and Card3 but that means that there is $18 left with a budget of $30.00 that should be allocated.

Well at this point there is a minimum payment reallocation which simply adds more money to the payment for the Card with

1. Remaining balance more than payment
2. Highest APR

In this case Card2's payment goes from $10.00 to $18.00 + $10.00 = $28.00

balance 1	balance 2	balance 3	Month
51	100	51	1
41	90	41	2
31	80	31	3
21	70	21	4
11	60	11	5
1	50	1	6
0	22	0	7
0	0	0	8

For the optimal payments, the reallocation isn't done manually, we simply compute the balances one a time and the linear programming functions take care of the calculation since the total balances are updated after each iteration.

Note that we barely spoke of maximum payments at all They are used as a constraint on the linear programming problem. So if a user provides a maximum payment that is less than the budget or the balance of a card, the suggested payment for that card will not go over the maximum payment even if there is room in the budget!

Minimum Payment Adjustment

The minimum payment will not remain the same if the balance decreases. This is one of the assumptions of this API. There is a constant rate calculated as minimum payment / balance that is applied to each balance to adjust the minimum payment since this is a constraint for the linear programming problem.

Say at month 6 the minimum payments have not changed for Card1. Then the constraints applied to the optimal solution would imply that despite a balance of only $1.00, a payment of at least $10.00 should be made. That makes no sense! So initially a flat rate of 10 / 51 ~ .2 is used to adjust the minimum payment at month 6. So .2 * 1 = .2 which then ease the constraints for the Card.

P.S: Many simple assumptions were made for the simplicity of this project. These APIs are best used for cards/loans with fixed APR (note APY is not being used) and no additional expenses etc.

For a user friendly experience, please checkout this tool. It is still under construction