# APR to APY Calculator

> Convert nominal APR into effective APY based on compounding frequency.

**Category:** Finance
**Keywords:** apr, apy, compounding, yield, finance, interest
**URL:** https://complete.tools/apr-to-apy-calculator

## How it calculates

The formula to convert APR to APY is given by: APY = (1 + (APR ÷ n))^n - 1, where APR is the annual percentage rate, n is the number of compounding periods per year, and APY is the annual percentage yield. In this formula, APR is divided by n to determine the interest rate per compounding period. The expression (1 + (APR ÷ n))^n calculates the effect of compounding interest, raising it to the power of n to reflect the total growth over one year. The final step subtracts 1 to yield just the yield portion of the equation. This mathematical relationship highlights how compounding frequency affects the overall yield on an investment or cost of a loan.

## Who should use this

Mortgage brokers comparing loan products for clients, financial analysts reviewing investment options for portfolios, accountants calculating effective interest rates for financial statements, and individuals assessing savings account yields from different banks can all benefit from this tool.

## Worked examples

Example 1: A savings account offers an APR of 5% compounded monthly. To find the APY, use the formula: APY = (1 + (0.05 ÷ 12))^12 - 1. First, calculate 0.05 ÷ 12 = 0.00416667. Then, (1 + 0.00416667)^12 = 1.0511619. Finally, subtract 1 to get APY = 0.0511619 or 5.12%. This means the effective yield on the savings account is 5.12%. Example 2: A personal loan has an APR of 8% compounded quarterly. Here, n = 4. Using the formula: APY = (1 + (0.08 ÷ 4))^4 - 1, we find 0.08 ÷ 4 = 0.02. Then, (1 + 0.02)^4 = 1.082856. Subtracting 1 gives APY = 0.082856 or 8.29%. This indicates that the effective interest cost of the loan is 8.29%.

## Limitations

This tool assumes the compounding frequency is consistent throughout the year. If the actual compounding frequency differs from the input (e.g., a loan with monthly compounding treated as annually), the results may be inaccurate. The calculator also may not account for fees associated with financial products, which can affect the overall yield. Additionally, precision is limited to the decimal points used in the calculation, which may lead to rounding errors in some cases. Finally, the tool does not consider tax implications on interest earned, which can significantly impact the real effective yield.

## FAQs

**Q:** How does compounding frequency affect the APY calculation?


**A:** Compounding frequency directly influences how often interest is calculated and added to the principal, impacting the total yield. More frequent compounding results in a higher APY.


**Q:** Can I use this calculator for non-annual compounding periods?


**A:** Yes, the calculator takes any compounding frequency (monthly, quarterly, etc.) into account, provided the correct value for n is inputted.


**Q:** What happens if I input a negative APR?


**A:** The calculator will still perform the calculation, but a negative APR typically indicates a loss rather than a gain, and the resulting APY may not be meaningful in practical scenarios.


**Q:** Is the APY always higher than the APR?


**A:** Generally, yes, APY accounts for compounding, which can make it higher than APR, except in cases where the APR is negative or the compounding effect is negligible.

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