💵 💵 Simple vs Compound Interest: Formula and Calculator Guide

Interest is the cost of using money — either what you pay to borrow it, or what you earn by lending or saving it. Two fundamentally different methods calculate interest: simple and compound. The difference between them, over long periods, can be the difference between modest savings and life-changing wealth — or between a manageable debt and an overwhelming one.

Simple Interest

Simple interest is calculated only on the original principal, never on accumulated interest. It grows linearly.

Simple Interest = P × r × t

Total Amount = P × (1 + r × t)

Where: P = Principal, r = Annual interest rate (as decimal), t = Time in years

Simple Interest Example

You deposit $5,000 in a savings account at 4% simple interest for 3 years.

• Interest = $5,000 × 0.04 × 3 = $600
• Total = $5,000 + $600 = $5,600

Simple interest is used for short-term loans, bonds that pay fixed coupons, and some personal loans.

Compound Interest

Compound interest is calculated on both the principal and the accumulated interest from previous periods. It grows exponentially — "interest on interest." This is the fundamental mechanism behind long-term wealth building.

A = P × (1 + r/n)^(n×t)

Where:

• A = Final amount
• P = Principal
• r = Annual interest rate (decimal)
• n = Number of compounding periods per year
• t = Time in years

Compound Interest Example

Same $5,000 at 4% for 3 years, compounded monthly (n=12).

• A = $5,000 × (1 + 0.04/12)^(12×3)
• A = $5,000 × (1.003333)^36
• A = $5,000 × 1.1272 = $5,636
• Compound interest earned: $636 (vs $600 simple interest)

The difference seems small at 3 years, but explodes over decades.

The Power of Compounding Over Time

$10,000 invested at 7% annual return:

At 30 years: simple interest yields $31,000. Monthly compounding yields $81,165 — 2.6× more from the same initial $10,000.

Compounding Frequency: Does It Matter?

The more frequently interest compounds, the more you earn (or owe). Common compounding periods:

• Annually (n=1): Most basic; simple bonds and CDs may compound annually
• Quarterly (n=4): Some savings accounts
• Monthly (n=12): Most savings accounts, mortgages, personal loans
• Daily (n=365): High-yield savings accounts, many credit cards
• Continuously: Theoretical limit; Formula: A = P × e^(rt)

The difference between monthly and daily compounding is usually small. The difference between annual and monthly compounding is more significant for long periods.

The Rule of 72

A quick mental math trick for estimating how long it takes to double money with compound interest:

Years to double = 72 ÷ Annual interest rate

• At 6%: 72 ÷ 6 = 12 years to double
• At 8%: 72 ÷ 8 = 9 years to double
• At 12%: 72 ÷ 12 = 6 years to double

The Rule of 72 also works in reverse for debt: credit card debt at 24% APR doubles in just 3 years if unpaid.

Compound Interest Against You: Debt

Compound interest is powerful for savings — and devastating for debt. Credit card interest typically compounds daily at rates of 18–29% APR.

Example: $5,000 credit card balance at 22% APR, minimum payments only:

• Monthly interest: ~$91.67 in the first month
• If minimum payment is $100, only $8.33 reduces the balance
• At this rate, paying off $5,000 takes years and costs over $6,000 in interest

The only counter to compound interest on debt is paying significantly more than the minimum — or eliminating the balance entirely.

APR vs. APY: Which Rate to Compare

• APR (Annual Percentage Rate): The nominal annual rate before compounding effects. Used for loans and credit cards.
• APY (Annual Percentage Yield): The effective annual rate after compounding. Used for savings accounts. APY is always higher than APR when compounding occurs more than once per year.

Formula: APY = (1 + APR/n)^n − 1

Example: 6% APR compounded monthly: APY = (1 + 0.06/12)^12 − 1 = 6.168%

When comparing savings accounts, always compare APY. When comparing loans, compare APR (and total interest paid).