Percentages in Finance: Interest Rates, Returns, and Inflation Explained

Financial news is full of percentages. The Fed raised rates by 25 basis points. Your 401(k) returned 11.3% last year. Inflation is 3.2%. What do these numbers actually mean?

Interest Rates

An interest rate is the cost of borrowing money (for loans) or the reward for lending it (for savings).

Annual Percentage Rate (APR): The yearly interest rate, not accounting for compounding within the year.

Annual Percentage Yield (APY): The actual annual return, accounting for compound interest. APY is always higher than APR when compounding is more frequent than annual.

Example: A savings account with 5% APR compounded monthly has an APY of 5.12%.

When comparing financial products: use APY for savings (you want to earn more), use APR for loans (you want to pay less).

Investment Returns

Total return: (End value - Start value + Dividends) ÷ Start value × 100

You invested $10,000. It grew to $11,500 and paid $200 in dividends.

Total return = ($11,500 - $10,000 + $200) ÷ $10,000 × 100 = 17%

Annualized return (CAGR): For multi-year investments, the annualized return smooths out year-to-year variation.

$10,000 grew to $14,000 over 4 years: CAGR = (14,000/10,000)^(1/4) - 1 = 8.78% per year

Basis Points: The 1/100 of a Percent

Financial professionals often use basis points (bps) instead of percentages for small rate changes.

1 basis point = 0.01% = 0.0001

100 basis points = 1%

Why? Saying "the Fed raised rates 25 basis points" is clearer than "0.25 percentage points" and avoids confusion with "25% increase in the rate."

Inflation

Inflation measures the percentage increase in the price level over time. A 3% inflation rate means prices are 3% higher than a year ago on average.

Real vs. nominal returns:

Nominal return: What your investment returned in dollar terms.

Real return: What you actually gained in purchasing power, after inflation.

Approximate real return = Nominal return - Inflation rate

Your savings account earns 4.5% but inflation is 3.2%. Real return ≈ 1.3%.

More precisely: Real return = ((1 + Nominal) ÷ (1 + Inflation)) - 1 = (1.045 ÷ 1.032) - 1 = 1.26%

Purchasing Power Over Time

At 3% annual inflation, the purchasing power of $100 changes:

• After 10 years: $74.41 in today's dollars
• After 20 years: $55.37 in today's dollars
• After 30 years: $41.20 in today's dollars

This is why keeping money in cash long-term is a losing strategy — inflation erodes its value.

Calculate any financial percentage with our Percentage Calculator.