Simple and Compound Interest Formula: Examples & Calculator

Simple and Compound Interest Formula

Understanding simple interest and compound interest is fundamental to personal finance, banking, investing, and professional accounting exams. While simple interest grows linearly, compound interest grows exponentially—and the difference can amount to thousands of dollars over time. This guide breaks down both formulas with step-by-step examples so you can calculate interest confidently. For the underlying concept, see our detailed guide on the time value of money and present value.

What Is Simple Interest?

Simple interest is calculated only on the original principal amount for each period. The interest earned does not get added back to the principal, so you earn the same dollar amount each period. It is commonly used for short-term loans, auto loans, and some fixed deposits.

Simple Interest Formula

Where:

• P = Principal (initial amount)
• r = Annual interest rate (as a decimal, e.g., 8% = 0.08)
• t = Time in years

The total amount after simple interest is: A = P + SI = P(1 + rt)

Simple Interest Example

Scenario: You deposit $10,000 in a fixed deposit at 6% annual simple interest for 3 years.

You earn exactly $600 each year—the interest does not change because it

What Is Compound Interest?

Compound interest is calculated on the principal and on the accumulated interest from previous periods. This creates an exponential growth pattern where your money earns interest on interest. It is the standard method for savings accounts, credit cards, mortgages, and most investment accounts.

Compound Interest Formula

Where:

• A = Final amount (principal + interest)
• P = Principal (initial amount)
• r = Annual interest rate (as a decimal)
• n = Number of times interest is compounded per year
• t = Time in years

The compound interest itself is: CI = A – P

Common Compounding Frequencies

is always calculated on the original $10,000.

Compound Interest Example 1: Annual Compounding

Scenario: You invest $10,000 at 6% compounded annually for 3 years.

Compare this with the simple interest result of $1,800. That extra $110.16 is the interest earned on interest—the compounding effect.

Compound Interest Example 2: Monthly Compounding

Scenario: Same $10,000 at 6%, but compounded monthly for 3 years.

Monthly compounding adds an extra $56.65 compared to annual compounding because interest is reinvested 12 times a year rather than once.

Simple Interest vs Compound Interest: Side-by-Side Comparison

The Power of Compounding Over Time

The longer your investment horizon, the more dramatic the compounding effect becomes. Here is what $10,000 grows to at 8% annual interest over different time frames:

After 30 years, compound interest produces nearly three times the return of simple interest on the same principal and rate. This is why financial advisors emphasise starting to invest early—even small amounts benefit enormously from long compounding periods.

Rule of 72: Quick Mental Math

The Rule of 72 is a shortcut to estimate how long it takes for money to double with compound interest:

For example, at 8% annual interest, your money doubles in approximately 72 ÷ 8 = 9 years. At 6%, it takes about 72 ÷ 6 = 12 years. This rule works well for rates between 2% and 15%.

Real-World Applications

1. Savings Accounts & Fixed Deposits

Most bank savings accounts and certificates of deposit (CDs) use compound interest. Understanding whether your bank compounds monthly, quarterly, or annually directly affects your effective yield. A 5% rate compounded monthly gives a higher effective annual rate (5.12%) than the same rate compounded annually.

2. Loans & EMIs

Home loans and personal loans typically use compound interest to calculate the total repayment. This is why even a small rate reduction can save you thousands over the life of your mortgage. The EMI (Equated Monthly Installment) formula is directly derived from compound interest principles, factoring in the principal, rate, and tenure.

3. Credit Card Debt

Credit cards often compound interest daily, which is why revolving debt grows so quickly. A $5,000 balance at 18% APR compounded daily can balloon to over $6,000 in just two years if only minimum payments are made.

4. Investment Returns & Retirement Planning

Investment portfolios grow through compound returns. A systematic investment plan (SIP) that compounds monthly over 20–30 years creates significant wealth, even with modest monthly contributions. This is the principle behind most retirement calculators and pension fund projections.

5. Corporate Finance & IFRS

In corporate accounting, compound interest underpins the calculation of present values for leases, bonds, and financial instruments. Under IFRS standards, the effective interest method (based on compound interest) is required for amortising financial liabilities. Key financial ratios, such as the interest coverage ratio, measure a company's ability to service its debt obligations.

How to Calculate Interest: Step-by-Step

Frequently Asked Questions

What is the simple interest formula?

Simple Interest = Principal × Rate × Time (SI = P × r × t). It calculates interest only on the original principal amount. For example, $5,000 at 4% for 2 years = $5,000 × 0.04 × 2 = $400 in interest.

What is the compound interest formula?

A = P(1 + r/n)^nt, where P is principal, r is the annual rate, n is compounding frequency, and t is time in years. The compound interest itself equals A – P. This formula accounts for interest earned on previously accumulated interest.

What is the difference between simple and compound interest?

Simple interest is calculated only on the original principal, producing linear growth. Compound interest is calculated on the principal plus accumulated interest, producing exponential growth. Over longer periods, compound interest generates significantly more returns (or costs, for borrowers).

How does compounding frequency affect returns?

More frequent compounding produces higher returns because interest is reinvested more often. Monthly compounding yields more than quarterly, which yields more than annual compounding—all at the same stated rate. The difference is captured by the Effective Annual Rate (EAR).

What is the Rule of 72?

The Rule of 72 is a quick estimation tool: divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 6%, money doubles in approximately 12 years. At 12%, it doubles in about 6 years.

Where is compound interest used in accounting?

Compound interest is used in calculating present values and future values, bond pricing, lease liability calculations under IFRS 16, loan amortisation schedules, and the effective interest method for financial instruments under IFRS 9.

How does compound interest relate to EMI calculations?

EMI (Equated Monthly Installment) calculations are built on compound interest. The EMI formula uses the principal, monthly interest rate, and number of months to determine a fixed payment that covers both interest and principal repayment over the loan tenure.

Preparing for Professional Exams?

Simple and compound interest formulas are tested across multiple certifications:

• CPA BEC: Time value of money calculations and financial analysis
• CMA Part 1: Financial planning, including present value and future value formulas
• ACCA FM: Investment appraisal and working capital management
• CFA Level 1: Quantitative Methods and Fixed Income sections

Eduyush offers comprehensive preparation resources for CMA USA and other professional certifications to help you master time value of money concepts.