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.
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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).
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