How Compound Interest Works in a Savings Account

APR (Annual Percentage Rate) is the stated rate before compounding. APY (Annual Percentage Yield) is the effective rate after compounding. APY ≥ APR, always.

Example: a bank offers 4.50% APR compounded daily. APY = (1 + 0.045/365)^365 – 1 = 4.603%. The difference seems tiny, but on $50,000 over 10 years, it means $500+ more.

When comparing savings accounts, always compare APY to APY. Banks are required by law (Truth in Savings Act) to disclose APY.

Each day, the bank calculates interest on your current balance (including all previously earned interest). The daily rate is APR ÷ 365.

Example: $10,000 at 4.5% APR compounded daily. Day 1 interest: $10,000 × (0.045/365) = $1.2329. Day 2 balance: $10,001.23. Day 2 interest: $10,001.23 × (0.045/365) = $1.2330.

The fractions of a penny add up. After one year: $10,000 × (1 + 0.045/365)^365 = $10,460.30. That is $10.30 more than simple interest would have given ($10,450).

$10,000 at 4.5% APY with zero additional deposits: After 10 years: $15,530. After 20 years: $24,117. After 30 years: $37,453.

Now add $200/month: After 10 years: $45,540. After 20 years: $104,200. After 30 years: $196,000.

The gap between "deposited" and "earned" widens dramatically over time. At 30 years, you deposited $82,000 but earned $114,000 in interest — that is compounding doing the heavy lifting.

A 4.5% APY vs. a 4.0% APY on $20,000 over 20 years: the 4.5% account yields $24,117; the 4.0% yields $21,911. That is a $2,206 difference from just 0.5%.

High-yield savings accounts (online banks) typically offer 1–2% more than traditional brick-and-mortar banks. The money is equally FDIC-insured.

Use the Retirement Savings Calculator to model different rates and see the long-term difference.