Nominal interest rate and effective interest rate converter 

This tool converts nominal interest rates to effective interest rates and vice versa. The compounding period and payment period can be set at different frequencies. Besides nominal interest rates and effective interest rates this tool also calculates the periodic interest rate. To convert the interest rates the following equations are used: Compound period equals payment period: Re = (1 + (R / N))^{N}  1 R = N * ((1 + Re)^{(1 / N)}  1) r = R / N Compound period is not equal to payment period: Re = (1 + (R / N))^{N}  1 r = ((1 + Re) ^ (1 / M)  1) R = r * M where:
Example 1: The nominal annual interest rate is 4.67% compounded quarterly. Question: What is the effective annual interest rate? Solution: Re = (1 + (R / N))^{N}  1 = (1 + (0.0467 / 4))^{4}  1 = 0.047524 Example 2: The effective annual interest rate is 3.5% compounded weekly. Question: What is the nominal annual interest rate? Solution: R = N * ((1 + Re)^{(1 / N)}  1) = 52 * ((1 + 0.035)^{(1 / 52)}  1) = 0.034413 Example 3: Saving bank A pays a nominal annual interest rate (APR) of 10% compounded semiannually. Savings bank B pays a nominal annual interest rate (APR) of 9.5% compounded quarterly. Question: Which bank offers the best effective annual interest rate (EAR)? Solution: Bank A: Re = (1 + (R / N))^{N}  1 = (1 + (0.10 / 2))^{2}  1 = 0.1025 Bank B: Re = (1 + (R / N))^{N}  1 = (1 + (0.095 / 4))^{4}  1 = 0.1027 Bank B offers the best savings return or Equivalent Annual Rate (EAR). Example 4: A savings bank pays 2.5% interest every 3 months. Question: What are the nominal and effective interest rates per year? Solution: R = r * N = 0.025 * 4 = 0.1 Re = (1 + (R / N))^{N}  1 = (1 + (0.1 / 4))^{4}  1 = 0.1038 Example 5: Bank A offers an effective annual interest rate (Re) of 6%. Bank B offers a nominal interest rate of 1.5% per quarter. Question: Which of these two banks offers the best return? Solution: Bank B: R = r * N = 0.015 * 4 = 0.06 Re = (1 + (R / N))^{N}  1 = (1 + (0.06 / 4))^{4}  1 = 0.061364 Bank B offers a better return. Example 6: The nominal interest rate of 10% compounded monthly. Question: Find the effective interest rate per payment period if the payment period is:
Re = (1 + (R / N))^{N}  1 = (1 + (0.10 / 12))^{12}  1 = 0.104713
