Pop Quiz, Hot Shot.

You have the following credit cards/checking accounts with the following attributes:

Card 1: 24.99% APR, 30-day grace period, $500 limit, No balance, 1.5% Cash back on purchases, accepts balance transfers; no cash back on balance transfers

Card 2: 19.99% APR, 30-day grace period, $900 limit, Current balance of $300 (accruing interest), does not accept balance transfers

Card 3: 10.5% APR, 15-day grace period, $1500 limit, current balance of $900(accruing interest), accepts balance transfers, balance transfer rate is 13.5%, with grace period

Checking account: 2.53% APY, Calculated on the average daily balance of the account

How do you optimize your monthly cash flow over several months with an income of X dollars per month, paid in 2 equal installments of X/2 over the course of each month, when you have monthly expenses of .75(X)?

You might be thinking, “Whoa, now. The SAT’s were a few years ago, this is awfully complex. Why would I need all this math?”

The answer of course is to maximize the resources you have. A 1.5% discount on your spending might not seem like much, but it’ll make for a nice start when you’re looking to save up.

Basically, this question is about being able to understand and allocate resources in an efficient manner. So, how do you solve this problem?

- Balances from Card 2 should be transferred to Card 3, and paid off on the last day of the grace period.
- Monthly expenses should be put on the Card 1 to earn cash back, and then transferred to Card 3 at the end of the grace period (to avoid interest and allow for an extra 15 days grace period),
- The existing balances should be paid off at a rate of .25(X) per month, to minimize interest.
- (Optional) Call Card 1’s issuer and ask for a limit increase,
- After balances are paid off, you should be earning 1.0253
^{(1/12)}* (1.5 X + .26125(X*N-1) + (previous months’ interest)) each month, since you now are able to keep your cash for ~45 days (1.5 months), and thanks to the cash back, you are spending 73.875% of your income on expenses instead of 75%. N represents the number of months since all cards were paid off. Card 2 would be kept open and paid off, both for emergencies, and to lower your utilization.

Right about now, most people are thinking, “What the What? I don’t even…”

Here’s a breakdown of what we did, step-by-step:

- Moved the high interest debt to a lower cost opportunity, including 15 days interest-free.
- Change the spending habit to put the monthly expenses on a card that gets cash back. This has the net effect of either lowering the amount you pay for things, meaning instead of spending $75 of every hundred dollars, you’re spending $73.875.
- Now, we’re aggressively attacking debt, meaning debt will get paid off in the shortest time frame possible with our available resources.
- With a low-limit card, a bit more breathing room will make sure you can afford to put as many of your expenses as possible on the card and earn cash back.
- This step is a projected balance for few months down the road, but here’s what’s going on:
- Your monthly account interest is 1/12 of 2.53% Annual Percentage Yield, so to get that, we use the compound interest formula of 1 + interest rate ^(period).
- We multiply our monthly account interest by the balance in the account, which is the sum of
- i. 1.5X – Three Bi-weekly paychecks (45 days)
- ii. .26125(X*N-1) – Your Monthly Savings Rate (100-73.875=26.125) times the total number of months (N) since you paid off your credit card debt, minus 1 (which is included in the three bi-weekly paychecks.
- iii. The sum of the interest paid to you for the last N-1 months.

All of this is a very powerful system. Now, instead of paying around $30 in interest each month, you’re getting $15 from the credit card company, usually applied to the balance of your purchases. Depending on the card, your own spending habits, and the offers available you could end up with double or even triple that amount. The key to all of this is ensuring you keep your credit cards paid off each billing cycle. By doing this, you’re holding on to your money as long as possible, being paid by companies for the privilege to loan you money interest-free, and earning interest.

Until next time, eat a little more debt.