Friday Fundamentals: Understanding APY and APR

Ever wonder what these numbers really mean — and how they can help you make smarter financial decisions?

What It Is

APY (Annual Percentage Yield)

APY tells you how much your savings will grow in one year, including compound interest. Compound interest means you earn interest on your money — and on the interest your money has already earned.

APR (Annual Percentage Rate)

APR tells you how much it costs to borrow money for one year. APR doesn’t show compounding the way APY does — it’s the yearly rate lenders use to calculate what borrowing will cost.

Why It Matters

APY

APY tells you how fast your savings can grow. A higher APY means your money earns more over time. Comparing APYs helps you choose accounts that grow your savings more effectively.

APR

APR shows you whether a loan or credit card is expensive or affordable. A lower APR means borrowing costs less. Comparing APRs helps you avoid paying unnecessary interest.

How to Use It

APY Example

Bank shows: 4.50% APY.

If you deposit $1,000, a 4.50% APY means your money will grow by a little more than $45 since APY includes both the basic interest and the small extra amount from compounding.

Simple math:

$1,000 × 4.50% = $45

What you end the year with:

About $1,045

Note: $1,045 is a very close estimate. It isn’t exact because simple math doesn’t calculate the compound interest. But for everyday use, the simple math is close enough. If you’re curious and love math, the exact formula is A = P(1 + r/n)ⁿ. Using that formula, $1,000 at 4.50% APY becomes about $1,045.99 after one year — less than $1 more than the simple $45 estimate.

APR Example

Lender shows: 10% APR.

If you borrow $1,000, a 10% APR means you’re paying about $100 more than you borrowed in interest for that year.

Simple math:

$1,000 × 10% = $100

Estimated total: $1,100

When simple math is exact

Simple math only works when the loan lasts one year and you repay the full amount in one lump sum at the end of the year. In that case, the total owed is $1,100.

Most people don’t borrow this way.

What usually happens with loans

Usually, people take out loans because they don’t have all the money upfront to purchase something — like a car or a house — and they want to borrow the money and pay it back in installments.

Most loans calculate interest monthly, and each payment goes toward the interest for that month and a portion of the amount you borrowed. Because the balance changes every month, the total interest ends up slightly different from the simple estimate.

Using amortization — which simply means paying off a loan little by little through monthly payments — the true cost of a one-year, $1,000 loan at 10% APR comes out to about $1,104 if you are paying in installments as agreed.

That’s only about $4 more than the simple $1,100 estimate — which is why simple math works just fine for short loans you’ll pay off within a year. But for loans that last longer than a year, simple math breaks down and the difference can grow into hundreds or thousands of dollars. That’s why it’s so important to look at the required disclosures from the lender to see the true total cost of the loan.

When loans last for more than one year

Most loans last for more than one year because you typically borrow money for things you can’t pay off right away — think a car or a house.

For these types of loans, interest is calculated monthly, based on the remaining balance, which changes every month as you make payments. This is why simple math cannot reasonably be used for multi-year loans.

Example: A 4-year car loan at 6% APR

Loan amount: $20,000

APR: 6%

Term: 4 years (48 months)

Simple math (wrong to apply in this situation):

$20,000 × 6% × 4 = $4,800

This looks simple — but it’s wrong, because the balance drops every month as you make payments.

Actual cost if you pay the car note on time each month:

A 4-year, $20,000 loan at 6% APR actually costs about $2,536 in total interest.

Note for math lovers: Here’s the standard amortization formula used to calculate monthly payments:

Payment = P \times \frac{r(1+r)^n}{(1+r)^n - 1}

Where:

P = loan amount

r = monthly interest rate (APR ÷ 12)

n = number of monthly payments

Difference:

Simple math estimate: $4,800

Actual interest: $2,536

Simple math overestimated by about $2,264.

Where to Find the True Cost of a Loan

Lenders are required to show you the true cost of a loan — including the total interest you’ll pay over the life of the loan — before you sign.

These required disclosures come in different forms depending on the loan type:

• Personal loans & credit cards: Truth-in-Lending Disclosure

• Car loans: Retail Installment Sale Contract

• Mortgages: Loan Estimate (LE) and Closing Disclosure (CD)

All of these must show:

• Total amount financed

• Total finance charge (total interest)

• Total of all payments

• APR

• Monthly payment

This is where you find the real cost — not from APR alone.

A Note Before You Go

It’s so important to understand these numbers — because with the swipe of a pen, you’re making financial decisions that can affect your money for years. The more you understand your money, the more power you have over what it can do for you.

Be careful out there, lovely.

Related Money Dearest Pillars

→ Debt Management

→ Saving & Investing

Disclosure: This is for education, not personal financial advice. Everyone’s money situation is different, and decisions should be based on personal research or speaking with a licensed professional.