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Interest is the compensation paid by a borrower to a lender for the use of money, expressed as a percentage or fixed amount. It serves as the backbone of most financial instruments worldwide.

There are two primary methods of calculating interest: simple interest and compound interest.

Simple Interest

Simple interest is calculated only on the original principal amount over a set period.

Example:
Derek borrows $100 (the principal) from a bank for one year at a 10% annual interest rate.

• Interest Calculation:$100×10%=$10$100×10%=$10
• Total Repayment After One Year:$100+$10=$110$100+$10=$110

If Derek borrows the same amount for two years with annual interest:$100+$10 (Year 1)+$10 (Year 2)=$120$100+$10 (Year 1)+$10 (Year 2)=$120

Simple Interest Formula:Interest=Principal×Interest Rate×TermInterest=Principal×Interest Rate×Term

For non-annual compounding frequencies (e.g., monthly or daily), adjust the formula:Interest=Principal×Interest Rate×TermFrequencyInterest=Principal×Interest Rate×FrequencyTerm​

While simple interest is straightforward, it is rarely used in real-world financial products. Most loans and investments use compound interest.

Compound Interest

Compound interest is calculated on the initial principal plus accumulated interest from previous periods, leading to exponential growth.

Example:
Derek borrows $100 for two years at 10% annual compound interest.

• Year 1:$100×10%=$10→ Total: $110$100×10%=$10→ Total: $110
• Year 2 (Interest on new balance):$110×10%=$11→ Total: $121$110×10%=$11→ Total: $121

Compared to simple interest (120),compoundinterestyieldsahigherrepayment(120),compoundinterestyieldsahigherrepayment(121) because interest earns additional interest.

Key Insight:
The more frequently interest is compounded (daily, monthly, quarterly), the greater the final amount. Continuous compounding (using mathematical limits) provides the highest possible return.

The Rule of 72

A quick mental shortcut to estimate how long it takes for money to double:Years=72Interest RateYears=Interest Rate72​

Example:
At 8% interest, doubling time ≈ 728=9872​=9 years.
Note: Best suited for interest rates between 6% and 10% but works reasonably for rates below 20%.

Fixed vs. Floating Interest Rates

• Fixed Rates: Remain constant over the loan/investment term.
• Floating Rates: Adjust based on a reference rate (e.g., the Federal Reserve’s benchmark or LIBOR).

Note: Most financial calculators (including ours) assume fixed rates.

Additional Factors Affecting Interest

1. Contributions
   • Regular deposits boost growth.
   • Timing matters: Contributions at the beginning of a compounding period earn slightly more than those at the end.
2. Taxation
   • Interest income (e.g., bonds, savings accounts) is often taxed.
   • Example: A 6% return over 20 years on 100yields∗∗100yields∗∗320.71 tax-free**, but only $239.78 after a 25% marginal tax rate.
3. Inflation
   • Reduces purchasing power over time (historically ~3% annually in the U.S.).
   • To grow real wealth, returns must outpace inflation + taxes.

Final Thoughts

Understanding interest—whether simple or compound—helps in making informed borrowing and investing decisions. Taxes and inflation further influence real returns, emphasizing the need for strategic financial planning.

For precise calculations, use our Interest Calculator, which accounts for contributions, compounding frequencies, and fixed rates.

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