Interest Rate

An interest rate is the percentage charged for borrowing money or paid on deposited funds. For borrowers, it represents the cost of debt; for lenders or savers, it’s the rate of return on funds provided.

Key takeaways
* Interest rates are expressed as percentages and often quoted annually (APR for loans, APY for deposits).
* Simple interest is calculated only on the principal. Compound interest is calculated on the principal plus accumulated interest.
* Loan rates reflect risk—lower risk borrowers and shorter terms generally get lower rates.
* Central banks and economic conditions (inflation, growth) are major factors in how interest rates are set.

What an interest rate means

When you borrow, the lender charges interest as compensation for lending funds and forgoing other uses of that money. When you deposit, the financial institution pays interest for the right to use your funds. The interest rate determines how much extra is paid or received over time.

Understanding principal, risk, and pricing
* Principal: the original amount borrowed or deposited.
* Cost of debt: the total interest charged to the borrower.
* Lender return: the interest that compensates the lender or saver.
* Risk assessment: lenders price loans based on the borrower’s creditworthiness; higher perceived risk → higher interest rate. Credit scores play a major role in determining the rate offered.

Simple interest

Simple interest is calculated only on the principal.

Formula:
Simple interest = principal × interest rate × time

Example:
A $300,000 loan at 4% simple annual interest for one year:
Interest = $300,000 × 0.04 × 1 = $12,000
Total repaid after one year = $312,000

For a 30-year loan at the same simple rate, interest would be:
$300,000 × 0.04 × 30 = $360,000

Compound interest

Compound interest accrues on both the principal and previously accumulated interest. Over longer periods, compounding produces substantially more interest than simple interest.

Formula:
Compound interest = p × [(1 + r)^n − 1]
where p = principal, r = interest rate per compounding period, n = number of compounding periods

Examples:
* A $10,000 loan at 5% compounded annually for 3 years:
Interest = $10,000 × [(1 + 0.05)^3 − 1] ≈ $1,576.25
* A $300,000 loan at 4% compounded over 30 years results in a much larger total interest (illustrative totals can exceed the original principal by a wide margin when compounded long-term).

Compound interest and savings

Compound interest benefits savers. Banks pay interest (APY) on deposits that compounds at specified intervals, rewarding account holders for allowing the bank to use their funds for loans. The APY reflects the effect of compounding and shows the actual annualized return on deposit accounts.

APR vs. APY

• APR (annual percentage rate) is the annual cost of borrowing and typically does not reflect intra-year compounding.
• APY (annual percentage yield) is the actual annual return on a deposit account, including the effect of compounding.

How interest rates are determined

Interest rates offered by banks are influenced by:
* Central bank policy: central banks (e.g., the Federal Reserve) set benchmark rates that influence market rates.
* Inflation: higher inflation tends to raise nominal interest rates.
* Economic conditions: strong demand and investment push rates up; weak demand or recessionary conditions tend to lower rates.
* Credit risk and loan term: lenders charge higher rates for riskier borrowers and for longer loan terms because of greater default risk and higher opportunity cost.

Why longer loans often have higher rates than shorter loans

Longer loans present greater default risk and higher opportunity cost (funds are tied up longer). Lenders typically charge extra for that additional uncertainty, so 30-year loans generally have higher rates than 15-year loans.

How central banks use interest rates

Central banks use short-term interest rates as a monetary policy tool:
* Raising rates makes borrowing more expensive, reduces spending and investment, and helps cool inflation.
* Lowering rates makes borrowing cheaper, encourages spending and investment, and can stimulate economic activity.

Why bond prices move inversely to interest rates

Bonds pay fixed coupons. When prevailing interest rates rise, new bonds offer higher coupons, so existing lower-coupon bonds fall in market price to remain competitive. Conversely, when rates fall, existing bonds with higher coupons become more valuable and trade at premiums.

Interest rates and lending disparities

Research has documented disparities in mortgage outcomes across racial and ethnic groups, including higher denial rates and, in some studies, slightly higher interest rates charged to certain minority borrowers. Multiple analyses and datasets show differing magnitudes and interpretations; some attribute observed differences to underwriting and pricing practices, while others emphasize borrower choices or other factors. Efforts such as automated underwriting and regulatory enforcement aim to reduce discriminatory outcomes, but disparities remain a focus of policymakers and researchers.

Conclusion

Interest rates are central to borrowing, saving, investing, and monetary policy. Understanding how rates are calculated (simple vs. compound), how they are presented (APR vs. APY), and the economic forces that drive them can help consumers and businesses make better financial decisions.