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Compound Interest Rate Converter

Instantly convert compound interest rate with our free converter. See conversion tables, formulas, and step-by-step explanations.

Reviewed by Manoj Kumar, Mathematics Educator

Reviewed by Manoj Kumar, Mathematics Educator

Formula

EAR = (1 + r/n)^n − 1

EAR = (1 + r/n)^n − 1 — Where EAR = Effective Annual Rate (APY), r = Nominal annual interest rate (decimal), and n = Number of compounding periods per year (365 for daily, 12 for monthly, 4 for quarterly, 1 for annually). This formula converts any nominal rate into its true annual equivalent so you can compare rates across different compounding frequencies on an apples-to-apples basis. To convert between two compounding frequencies, first solve for EAR, then solve the inverse: r_new = n_new × ((1 + EAR)^(1/n_new) − 1). The future value of monthly contributions uses FV = PMT × ((1 + r/12)^(12t) − 1) / (r/12) since contributions are made monthly.

Worked Examples

Example 1: Retirement Savings Growth

Problem:You invest $10,000 today and add $500/month at 7% annual return for 30 years. How much will you have?

Solution:FV of initial $10,000 = $10,000 × (1 + 0.07/12)^(12×30) = $10,000 × 8.116 = $81,165\nFV of $500/month = $500 × ((1.005833)^360 - 1) / 0.005833 = $500 × 1,219.97 = $609,985\nTotal = $81,165 + $609,985 = $691,150\nTotal contributed = $10,000 + $500 × 360 = $190,000\nInterest earned = $691,150 - $190,000 = $501,150

Result:Future Value: $691,150 | Contributed: $190,000 | Interest: $501,150 (264%)

Example 2: Early vs Late Start Comparison

Problem:Person A starts at 25, invests $300/month for 40 years. Person B starts at 35, invests $300/month for 30 years. Both earn 7%.

Solution:Person A (40 years): FV = $300 × ((1.005833)^480 - 1) / 0.005833 = $791,957\nTotal contributed: $300 × 480 = $144,000\nInterest: $647,957\n\nPerson B (30 years): FV = $300 × ((1.005833)^360 - 1) / 0.005833 = $365,991\nTotal contributed: $300 × 360 = $108,000\nInterest: $257,991

Result:10 years earlier = $425,966 MORE (2.16x) with only $36,000 extra invested

Frequently Asked Questions

What is a realistic rate of return to use?

Different financial products use different compounding conventions, and knowing them helps you interpret rates correctly. Savings accounts and money-market accounts: typically compound daily, advertise APY. U.S. mortgages and most consumer loans: compound monthly, advertise APR. Canadian mortgages: compound semi-annually by law. U.S. Treasury bonds and most government securities: compound semi-annually. Corporate bonds: compound semi-annually, quoted as a semi-annual rate × 2. Credit cards: compound daily, quoted as an annual APR. Certificates of deposit (CDs): vary — daily, monthly, or at maturity. Knowing the convention for each product lets you use this converter to produce a true apples-to-apples EAR comparison before committing funds.

What is the difference between simple and compound interest?

Simple interest is calculated only on the original principal (SI = P × r × t). Compound interest applies to the growing balance — each period's earned interest is added to principal before the next calculation (A = P(1 + r/n)^nt). On $10,000 at 8% over 20 years, simple interest yields $26,000 while annual compounding yields $46,610 — a 79% difference. High-yield accounts advertise APY to reflect compounding rather than the lower nominal rate.

References

Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy