Interest Rate

Definition: An interest rate is the cost of borrowing money, expressed as a percentage of the amount borrowed, or equivalently the return earned by a lender or saver.

How It Works

Interest is the price of money over time.

A borrower pays it because they get to use funds now instead of later.
A lender earns it as compensation for delaying their own spending.
A lender also earns it as compensation for the risk the borrower might not repay.
Every interest rate has three components:
- Principal — the amount borrowed or deposited.
- Rate — the percentage charged per period, usually annualized.
- Term — how long the money is borrowed or held for.
Rates are almost always quoted as an annual percentage, even for short loans.
- A 6% annual rate on a one-month loan charges roughly 0.5% for that month.
Three forces set the level of any specific interest rate.

What Sets a Given Rate

The central bank’s policy rate — the base cost of money in the economy, set to manage inflation and growth. See Central Bank and Monetary Policy.
Inflation expectations — lenders demand a higher rate if they expect repayment money to buy less than it does today.
Credit risk — the perceived chance a specific borrower defaults.
- Riskier borrowers pay a spread above the base rate.
- The spread compensates lenders for that extra risk.
Banks start from a benchmark rate, such as a central bank rate or SOFR (Secured Overnight Financing Rate).
Banks then add a margin based on the borrower’s creditworthiness, collateral, and the lender’s own cost of funds.

Key Formulas

Simple Interest

Interest is charged only on the original principal, never on interest already earned: $I = P \times r \times t$

$P$ is the principal.
$r$ is the annual interest rate, as a decimal.
$t$ is time, in years.

Compound Interest

Interest is charged on the principal and on previously accumulated interest, so balances grow faster over time. See Compound Interest. $A = P\left(1 + \frac{r}{n}\right)^{nt}$

$A$ is the final amount after interest.
$n$ is the number of compounding periods per year.
$t$ is the number of years the money is invested or owed.

Nominal vs. Real Interest Rate — the Fisher Equation

The rate a bank quotes (the nominal rate) overstates the true purchasing-power gain when inflation is high. $1 + i = (1 + r)(1 + \pi)$ For everyday use this is commonly approximated as: $r \approx i - \pi$

$i$ is the nominal rate.
$r$ is the real rate.
$\pi$ is the inflation rate.
If a savings account pays 4% nominal interest and inflation is 3%, the real return is only about 1%.
See Real vs Nominal Value for more on this distinction.

Types of Interest Rates

Fixed rate — locked for the life of the loan or deposit.
- Payments never change, protecting the borrower if rates rise.
- The borrower doesn’t benefit if rates fall, unless they refinance.
Variable (floating) rate — reset periodically based on a benchmark.
- Payments rise and fall with market conditions.
- Common on credit cards and adjustable-rate mortgages.
Nominal rate — the stated rate before adjusting for inflation.
Real rate — the nominal rate adjusted for inflation, reflecting actual purchasing-power growth.
Simple vs. compound rate — whether interest accrues only on principal, or on principal plus prior interest.
Discount rate — the rate the central bank charges commercial banks for short-term emergency borrowing, distinct from the policy rate used to guide the broader economy.
Policy rate — the rate a central bank sets to influence the entire economy.
- Example: the U.S. federal funds rate, or the ECB’s deposit rate.
- Nearly every other rate in the economy is priced relative to this one.
Prime rate — the rate commercial banks charge their most creditworthy customers.
- Traditionally a few percentage points above the central bank’s policy rate.
APR (Annual Percentage Rate) — the yearly cost of a loan including certain fees.
APY (Annual Percentage Yield) — the effective annual return on a deposit once compounding is included.
- APY is always at least as high as the stated nominal rate.

Common Benchmark Rates

Benchmark	Set By	Typical Use
Federal funds rate	U.S. Federal Reserve	Overnight bank-to-bank lending; the base for most U.S. rates
SOFR	Market-derived, overseen by the Fed	Replaces LIBOR as the reference for many loans and derivatives
Prime rate	Individual commercial banks	Best-customer lending rate, usually a fixed spread above the policy rate
10-year Treasury yield	Bond market	Benchmark for long-term borrowing, including many mortgage rates
Discount rate	Central bank	Emergency short-term lending to commercial banks

Why It Matters

For Borrowers and Savers

A mortgage, car loan, or credit card rate directly determines total financing cost.
A few percentage points of difference can mean tens of thousands of dollars over a loan’s life.
The rate on savings accounts, CDs, and bonds determines how fast idle cash grows.
It also determines whether savings grow faster or slower than inflation erodes them.

For Investors and Businesses

Higher rates make bonds and cash more attractive relative to stocks.
Higher rates raise the discount rate used to value future company earnings.
A higher discount rate tends to pull stock prices down. See Stock Market.
The cost of borrowing to expand, hire, or buy equipment rises and falls with rates.
This directly shapes corporate investment decisions.

For Policymakers

Interest rates are the primary lever central banks use to manage the economy.
Raising rates cools an overheating economy.
Cutting rates stimulates a sluggish one.
This makes rates central to both monetary policy and Fiscal Policy debates.

How a Rate Change Ripples Through the Economy

A single central bank decision travels through several stages before it’s felt by ordinary borrowers and savers.

The central bank raises or lowers its policy rate.
Banks adjust the rates they charge each other for short-term overnight lending.
Commercial banks reprice the prime rate offered to their best customers.
Variable-rate loans (credit cards, adjustable mortgages) reprice within one or two billing cycles.
New fixed-rate loans (mortgages, auto loans) are issued at the new prevailing rate.
Savings account and CD rates adjust, though usually more slowly than loan rates.
Bond prices adjust immediately, since existing bond yields must stay competitive with new rates.
Stock valuations adjust as investors recompute the discount rate on future earnings.

Each stage happens on a different timeline, which is why rate changes take months to fully work through an economy — a lag central banks explicitly account for when setting policy.

Common Pitfalls

Confusing the stated rate with the real return. A 5% CD sounds attractive, but if inflation is 6%, the saver is losing purchasing power even as the account balance grows.
Ignoring compounding frequency. A 12% annual rate compounded monthly yields more than the same rate compounded annually.
Treating APR and APY as interchangeable. APR is generally used for borrowing costs and excludes compounding; APY is used for deposit yields and includes it.
Assuming rates only matter to borrowers. Rates also set the discount rate for valuing future cash flows, which is why rate changes move stock and bond markets even for people who hold no debt at all.
Overlooking that “the interest rate” is not one number. At any moment there are many different rates in the economy — savings, mortgage, credit card, government bond — each carrying its own spread for risk and term.
Expecting instant transmission. Because a policy rate change takes months to fully ripple through banks, loans, and asset prices, judging its effect too early can lead to the mistaken conclusion that “the rate hike didn’t work.”

Example

A saver deposits $10,000 into a savings account paying a 5% nominal annual interest rate, compounded monthly.

Using the compound interest formula with $P = 10{,}000$ , $r = 0.05$ , $n = 12$ , and $t = 1$ : $A = 10{,}000\left(1 + \frac{0.05}{12}\right)^{12} \approx 10{,}511.62$

The account earns about $511.62 in interest over the year.
That’s slightly more than the $500 a simple 5% calculation would suggest.
The difference comes from interest being earned on interest along the way.
If inflation that year runs at 3%, the saver’s real return is only about 2%.
Their money grew, but their actual buying power grew far more slowly than the account balance implies.
This gap between nominal growth and real growth is exactly why the Fisher equation matters for anyone comparing rates across different inflation environments.

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