Equivalent Rate Calculator – AER

To convert an interest rate from one compounding frequency to another, the calculator utilizes compound interest formulas that preserve the true growth of money over time. The primary equation used to find an equivalent rate with a new compounding frequency is: EqRate = NewCompFreq * ((1 + NomIntRate / CompFreq) ^ (CompFreq / NewCompFreq) - 1). Additionally, to find the true effective annual interest rate (AER), the tool applies the formula: EffIntRate = ((1 + NomIntRate / CompFreq) ^ CompFreq - 1). Here, NomIntRate is the stated annual rate, CompFreq is the original compounding periods per year, and NewCompFreq represents the target compounding frequency.

Imagine you have a savings product offering a nominal interest rate of 6% (NomIntRate = 0.06) compounded monthly (CompFreq = 12). You want to find out what the equivalent interest rate would be if the interest compounded daily (NewCompFreq = 365). First, divide the nominal rate by the original frequency: 0.06 / 12 = 0.005. Next, add 1 to get 1.005. Raise this result to the power of the ratio of the frequencies (12 / 365 ≈ 0.032877), which gives approximately 1.0001642. Subtract 1 to get 0.0001642, and finally, multiply by the new compounding frequency of 365. This yields an equivalent daily compounding rate of approximately 5.992%, demonstrating how frequent compounding alters nominal yields.

Always ensure that you enter the nominal interest rate as a decimal or percentage consistently according to the prompt. When comparing financial products, remember that a higher compounding frequency will always yield a slightly higher effective return for investments and a higher total cost for loans. Pay close attention to whether the product uses nominal rates or effective annual rates (AER) in its marketing disclosures to avoid miscalculating your potential earnings or debts.