How to Calculate Compound Interest and Loan Payments
Understanding compound interest is essential for financial planning. Learn formulas for savings growth, loan amortization, and investment returns.
Key Takeaways
- Simple interest is calculated only on the principal amount.
- A = P(1 + r/n)^(nt) where P is principal, r is annual rate, n is compounding frequency, and t is years.
- Loan payments use the annuity formula: M = P[r(1+r)^n] / [(1+r)^n - 1].
- To estimate how long it takes to double your money, divide 72 by the annual interest rate.
Percentage Calculator
Calculate percentages, increases, decreases, and ratios
Simple vs Compound Interest
Simple interest is calculated only on the principal amount. Compound interest is calculated on the principal plus accumulated interest. Over time, compounding creates exponential growth — Einstein reportedly called it the eighth wonder.
The Compound Interest Formula
A = P(1 + r/n)^(nt) where P is principal, r is annual rate, n is compounding frequency, and t is years. Monthly compounding (n=12) produces more than annual compounding (n=1) for the same rate.
Compounding Frequency Impact
| Frequency | $10,000 at 5% for 10 years |
|---|---|
| Annual | $16,288.95 |
| Monthly | $16,470.09 |
| Daily | $16,486.65 |
| Continuous | $16,487.21 |
Loan Amortization
Loan payments use the annuity formula: M = P[r(1+r)^n] / [(1+r)^n - 1]. Early payments are mostly interest; later payments are mostly principal. An amortization schedule shows this split for each payment.
Rule of 72
To estimate how long it takes to double your money, divide 72 by the annual interest rate. At 6%, money doubles in approximately 12 years (72/6 = 12).
Công cụ liên quan
Hướng dẫn liên quan
How to Use Scientific Notation and Number Formatting
Scientific notation makes very large and very small numbers manageable. This guide covers notation systems, significant figures, and formatting conventions used in science, engineering, and finance.
Unit Conversion Best Practices for Developers
Incorrect unit conversions have caused spacecraft crashes and medical errors. This guide covers best practices for implementing unit conversions in software, including precision handling and common pitfalls.
Percentage Calculations: Common Formulas and Pitfalls
Percentage calculations appear simple but hide common errors, especially around percentage change, percentage points, and compound percentages. This guide clarifies the math behind everyday percentage problems.
Matrix Operations: A Visual Guide for Developers
Matrices are fundamental to graphics, machine learning, and data processing. This guide explains matrix addition, multiplication, transposition, and inversion with visual examples and practical applications.
Troubleshooting Floating-Point Precision Errors
Floating-point arithmetic produces surprising results that can cause bugs in financial calculations, comparisons, and cumulative operations. This guide explains why these errors occur and how to handle them.