A credit card had an APR of 23.51% all of last year and compounded interest daily. What was the credit card's effective interest rate(EIR) last year? Show your work.
{[1 + (.2351 / 365)]^365} - 1
A credit card had an APR of 14.86% all of last year, and compounded interest daily. What was the credit cards effective interest rate last year
To find the credit card's effective interest rate (EIR) with a given APR and daily compounding, follow these steps:
Step 1: Convert the APR to a decimal. Divide the APR by 100 to convert it from a percentage to a decimal.
APR = 23.51% = 0.2351
Step 2: Determine the interest rate per compounding period. Since the credit card compounds interest daily, divide the APR by 365 (the number of days in a year).
Daily Interest Rate = 0.2351 / 365
Step 3: Calculate the effective interest rate (EIR) using the formula:
EIR = (1 + Daily Interest Rate)^365 - 1
Let's plug in the values and calculate the EIR:
EIR = (1 + 0.2351 / 365)^365 - 1
Using a calculator or a spreadsheet, we can evaluate this expression to find the EIR.
EIR ≈ 0.2491
Therefore, the credit card's effective interest rate (EIR) last year was approximately 24.91%.