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Chapter 3

Credit & Credit Scores

Card interest, the minimum payment, and what a score is worth

A credit card is a loan you take out by accident. The rate is quoted per year and charged per day, which is what makes the real cost hard to feel.

Chapter 3 · The idea

A yearly rate, charged daily

An APR is an annual percentage rate, but interest is applied to the balance every day of the billing cycle. To use it you first have to break it down into the rate that is actually charged.

rdaily=APR365r_{\text{daily}} = \frac{\text{APR}}{365}

Then interest for a cycle is that rate, on the balance, for as many days as the cycle runs:

I=P×rdaily×tI = P \times r_{\text{daily}} \times t
Average Daily Balance
What card issuers actually multiply by. It is the balance on each day of the cycle, averaged over the cycle — so a payment made on day 2 saves you far more interest than the same payment made on day 28. When the balance never changes, as below, the average daily balance is just the balance.
Chapter 3 · Worked problem

One month of ignoring the bill

The problem
Sam maxes out his first credit card with a $1,000 balance. The card has a 24% APR. If he makes no payment at all for a 30-day billing cycle, how much interest is added?
Working1 / 4
  1. Break the annual rate down to a daily onerdaily=0.24365≈0.0006575r_{\text{daily}} = \frac{0.24}{365} \approx 0.0006575
Chapter 3 · The minimum

The minimum payment is designed to keep you paying

A card statement shows a minimum payment — usually about 1% of the balance plus that month's interest, and never less than $25. It is calculated so that the balance shrinks, slowly enough that the card keeps earning interest for years. Paying it is not the same as paying the bill.

The usual minimumminimum=max⁡($25,  0.01×B+I)\text{minimum} = \max\left(\$25,\; 0.01 \times B + I\right)
Figure 7The red line is the balance if Sam pays only the minimum each month; the blue line is the same balance at a fixed payment of your choosing. Drag the fixed payment down toward the minimum and watch the months run away.
The problem
Sam's $1,000 balance at 24% APR. If he pays only the minimum every month, how long does it take to clear, and what does it cost? Compare with a fixed $50 a month.
The first month1 / 3
  1. Interest for the month, at APR over twelveI=1000×0.2412=20I = 1000 \times \frac{0.24}{12} = 20
And the rest, month by month1 / 4
  1. Each month the minimum shrinks with the balance, until it reaches the $25 floormonths 1 to 18: B→0.99 B\text{months 1 to 18: } B \to 0.99\,B
Chapter 3 · The score

What a credit score is made of

A credit score is a prediction of whether you will repay, built from the file the bureaus keep on you. The FICO version, which most lenders use, weights five things — and two of them are most of it.

The five parts
  1. Payment history — 35%
    Whether every bill was paid on time. One payment thirty days late stays on the file for seven years.
  2. Amounts owed — 30%
    Mostly utilization: balances as a share of limits, across all cards. Under 30% is the usual target; under 10% is better.
  3. Length of history — 15%
    The age of the oldest account and the average age of all of them. The reason to keep an old card open with nothing on it.
  4. New credit — 10%
    Recent applications. Each hard inquiry costs a few points for about a year.
  5. Credit mix — 10%
    Having both revolving credit and an installment loan. Not worth taking out a loan to get.
The problem
Ava has two cards: a $2,000 limit with a $1,500 balance, and a $3,000 limit with a $300 balance. What is her utilization, and how much does she need to pay to bring it under 30%?
Working1 / 5
  1. Add up the limits2000+3000=50002000 + 3000 = 5000
Chapter 3 · The price of it

What a score is worth in dollars

The score is a price. A lender sets the rate on a loan from it, and the gap between a good score and a poor one is not a few points of interest — on a car loan it is several thousand dollars over the term.

The problem
Two people borrow $20,000 for a car over 60 months. One has a good score and is offered 6%. The other has a poor score and is offered 14%. What is the difference?
Working1 / 5
  1. The payment formula from Chapter 4M=P r(1+r)n(1+r)n−1M = P\,\frac{r(1+r)^n}{(1+r)^n - 1}

Interest of $3,199 on the good score and $7,922 on the poor one, for the same car. The poor score bought the same thing at a price nearly $5,000 higher, and paid it in instalments so that it never looked like a price.