How to Calculate APR and EAR for Short-term and Payday Loans

What is the APR and EAR for a short-term loan with a daily interest rate of 1.3%?

What is the actual rate of interest you would be paying for this loan?

What is the APR and EAR for a payday loan with a finance charge of $20 for every $100 borrowed?

If the loan must be repaid in two weeks, what are the APR and EAR?

APR and EAR Calculation for Short-term Loan

For the short-term loan with a daily interest rate of 1.3%, the APR is 474.5% and the EAR is approximately 860.29%.

APR and EAR Calculation for Payday Loan

For the payday loan with a finance charge of $20 for every $100 borrowed, the APR and EAR are both 52%.

For the short-term loan with a daily interest rate of 1.3%, we can calculate the Annual Percentage Rate (APR) and the Effective Annual Rate (EAR) as follows:

APR = Daily interest rate * 365

= 1.3% * 365

= 474.5%

To calculate the EAR, we need to consider compounding. Since the loan charges interest daily, the EAR can be calculated using the formula:

EAR = (1 + (Daily interest rate / 100))^365 - 1

= (1 + (1.3% / 100))^365 - 1

≈ 860.29%

The actual rate of interest you would be paying for the short-term loan is 1.3% per day.

For the payday loan where the finance charge is $20 for every $100 borrowed, and it must be repaid in two weeks, we can calculate the APR and EAR as follows:

APR = (Finance charge / Loan amount) * (Number of rollovers / Total loan period) * 100

= ($20 / $200) * (52 / 1) * 100

= 52%

Since the loan period is two weeks, the EAR will be equal to the APR because there are no compounding periods.

Therefore, the APR of the payday loan is 52% and the EAR is also 52%.

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