Money, First Principles

What are you about to decide?

Curious what a choice really costs? Move a slider and see the math for yourself. Free, no sign-up, nothing to sell.

Or see where money grows, shrinks and grows against you

Try it: a car loan at 9.00% APR (9.38% APY)

$30,000
72 months

Compared with a 48-month loan, you'd pay

$3,101 more in interest

$540.77 a month instead of $746.55. That's about 6 of your payments.

Use your own numbers

What happens to the same money in three different places?

Invested money can grow, because it earns returns on its returns. That's called compounding. Cash stays the same number, but rising prices mean it buys less each year. Card debt compounds against you: interest is added to what you owe. Move the sliders to see all three side by side.

After 10 years, in today's dollars

Invested
$0
Kept as cash
$0
Card debt owed
$0

The same amount goes in each bucket.

Show rates as

"As quoted" shows each rate the way lenders and banks quote it. Results don't change.

APR vs. APY: why the same rate has two numbers

APR (annual percentage rate) is the yearly rate before compounding.APY (annual percentage yield) is what you actually pay or earn in a year once interest starts charging, or earning, interest of its own.

Lenders quote APR because it's the smaller number. Banks quote savings in APY because it's the bigger one. A 9.00% APR car loan charged monthly costs 9.38% a year. A 24.00% APR card charged daily costs 27.11%. A 5.00% APY savings account is a 4.89% APR.

To compare any two rates fairly, put them in the same unit. "Show rates as" switches every rate on the page; the results don't change, because the rate underneath doesn't.

Kind of rateQuoted asHow it's applied
Car, mortgage and personal loansAPRAPR ÷ 12, each month
Credit cardsAPRAPR ÷ 365, each day, compounded
SavingsAPYMonthly, from the APY
Investment returnsYearly (APY basis)Monthly: (1 + rate)1/12 − 1

A loan's APR can include some fees as well as interest, so turning it into an APY here covers interest only. Inflation is always a plain yearly rate.

What an investment earns in a year, counting compounding. 7% is an illustration, not a promise.

How fast prices rise in a year. It makes each dollar buy a little less every year.

The yearly rate a card quotes. 22% is an illustration.

Card payments

With no payments, the balance compounds untouched.

An illustration, not a promise or advice. Real returns, inflation and card rates change over time.

See the year-by-year table
YearInvestedKept as cashCard debt owed
Show the math
  • The return and inflation are true yearly rates. Each is applied monthly at the rate that adds up to it over 12 months: (1 + yearly rate)1/12 − 1. "Today's dollars" means each future amount is divided by (1 + inflation)years, so you can compare it to what money buys now.
  • Invested: amount × (1 + return)years, in today's dollars. No new money added, no taxes or fees.
  • Kept as cash: the amount earns nothing, so its value is the amount in today's dollars.
  • Owed on a card: the card charges APR ÷ 365 each day, compounded, so a month's interest is balance × ((1 + APR ÷ 365)365/12 − 1). With no payments, that interest piles onto the balance. With payments on, each month pays the minimum, that month's interest plus 1% of the balance but at least $27, plus any extra. The line shows what's been paid so far plus what's still owed, in today's dollars. When payoff takes longer than the years shown, the payoff time and total interest keep counting past the chart, in actual dollars. No new purchases, no fees.
  • The minimum-payment formula is Capital One's, from its cardholder agreement:Capital One, Credit Card Agreement for Cabela’s Cards (Oct 1, 2017), in the CFPB credit card agreement database. Other cards use different floors; your statement shows your card's formula.

Why does every money decision land in one of three buckets?

Most of us run money on a cash basis: money comes in today and goes out tomorrow. But every dollar you keep or owe is quietly doing one of three things over time. Knowing which one tells you what a choice really costs, long after the day you make it.

  1. Compounds for you

    Investments and other things that earn money. Their earnings start earning too, so growth speeds up the longer you wait.

  2. Shrinks on its own

    Cash sitting still. The number doesn't change, but inflation (prices rising over time) means it buys a little less every year.

  3. Compounds against you

    Debt. Interest gets added to what you owe, and then you're charged interest on that interest too.

Where can I get free help from someone who isn't selling anything?

These government agencies and nonprofits offer free, trustworthy help with credit, debt, investing and taxes. None of them earns money from the choice you make. If you want advice about your own situation, they can also point you to a qualified professional.

See all trusted resources