Calculating Daily Interest

Oct 13, 2025 by wbrum.org 96 views

Introduction

Robert just got a new credit card and immediately made a purchase for $\$2750$ . The card offers a 0% APR for the first 60 days and a 17.99% APR afterward, compounded daily. Robert doesn't expect to pay off the $\$2750$ balance on time, and he's worried about the interest charges that will be applied to his account. In this article, we'll explore how credit card APR and compounding interest work, and what Robert can expect to pay in interest charges.

What is APR?

APR stands for Annual Percentage Rate, which is the interest rate charged on a credit card balance over a year. In the case of Robert's credit card, the APR is 17.99% after the first 60 days. This means that if Robert doesn't pay off his balance in full, he'll be charged 17.99% interest on the outstanding balance each year.

Compounding Interest

Compounding interest is a process where interest is added to the principal balance, and then interest is charged on the new balance. In the case of Robert's credit card, interest is compounded daily, which means that interest is charged on the outstanding balance every day.

Daily Compounding Formula

The formula for daily compounding interest is:

A = P(1 + r/n)^(nt)

Where:

A is the amount of money accumulated after n days, including interest
P is the principal amount (the initial amount borrowed)
r is the annual interest rate (in decimal form)
n is the number of times that interest is compounded per year
t is the time the money is invested for, in days

Calculating Daily Interest

To calculate the daily interest, we need to divide the annual interest rate by 365 (the number of days in a year). In this case, the annual interest rate is 17.99%, so the daily interest rate is:

17.99%/365 = 0.0491% per day

Calculating Total Interest

To calculate the total interest charged over a period of time, we need to multiply the daily interest rate by the number of days. In this case, we want to calculate the total interest charged over 60 days.

Total interest = 0.0491% per day x 60 days = 2.946%

Calculating Total Amount

To calculate the total amount owed after 60 days, we need to add the total interest to the principal amount.

Total amount = Principal amount + Total interest = $\$2750$ + $\$2750$ x 2.946% = $\$2750$ + $\$81.18$ = $\$2831.18$

Conclusion

In this article, we've explored how credit card APR and compounding interest work. We've calculated the daily interest rate, total interest, and total amount owed after 60 days. Robert can expect to pay $\$81.18$ in interest charges over the first 60 days, and a total amount of $\$2831.18$ .

What's Next?

Robert should consider paying off his balance in full before the 60-day promotional period ends. If he can't pay off the balance in full, he should try to make as many payments as possible during the promotional period to minimize the interest charges.

Additional Tips

Always read the fine print on credit card agreements to understand the terms and conditions.
Consider using a credit card with a 0% APR promotional period to save on interest charges.
Make multiple payments during the promotional period to minimize interest charges.
Pay off your balance in full before the promotional period ends to avoid interest charges.

References

Federal Reserve. (2022). Credit Card Interest Rates.
Consumer Financial Protection Bureau. (2022). Credit Cards.
Investopedia. (2022). Compounding Interest.
Frequently Asked Questions About Credit Card APR and Compounding Interest ====================================================================

Q: What is the difference between APR and interest rate?

A: The APR (Annual Percentage Rate) is the interest rate charged on a credit card balance over a year, while the interest rate is the rate charged on the outstanding balance each month. The APR is usually higher than the interest rate.

Q: How does compounding interest work?

A: Compounding interest is a process where interest is added to the principal balance, and then interest is charged on the new balance. In the case of credit cards, interest is compounded daily, which means that interest is charged on the outstanding balance every day.

Q: What is the formula for daily compounding interest?

A: The formula for daily compounding interest is:

A = P(1 + r/n)^(nt)

Where:

A is the amount of money accumulated after n days, including interest
P is the principal amount (the initial amount borrowed)
r is the annual interest rate (in decimal form)
n is the number of times that interest is compounded per year
t is the time the money is invested for, in days

Q: How do I calculate the daily interest rate?

A: To calculate the daily interest rate, you need to divide the annual interest rate by 365 (the number of days in a year). For example, if the annual interest rate is 17.99%, the daily interest rate would be:

17.99%/365 = 0.0491% per day

Q: How do I calculate the total interest charged over a period of time?

A: To calculate the total interest charged over a period of time, you need to multiply the daily interest rate by the number of days. For example, if the daily interest rate is 0.0491% and the number of days is 60, the total interest charged would be:

Total interest = 0.0491% per day x 60 days = 2.946%

Q: How do I calculate the total amount owed after a period of time?

A: To calculate the total amount owed after a period of time, you need to add the total interest to the principal amount. For example, if the principal amount is $\$2750$ and the total interest is $\$81.18$ , the total amount owed would be:

Total amount = Principal amount + Total interest = $\$2750$ + $\$2750$ x 2.946% = $\$2750$ + $\$81.18$ = $\$2831.18$

Q: What happens if I don't pay off my credit card balance in full?

A: If you don't pay off your credit card balance in full, you'll be charged interest on the outstanding balance. The interest rate will be applied to the balance, and you'll be charged a fee for late payment.

Q: Can I avoid paying interest on my credit card balance?

A: Yes, you can avoid paying interest on your credit card balance by paying off the balance in full before the due date. You can also consider using a credit card with a 0% APR promotional period to save on interest charges.

Q: What are some tips for managing credit card debt?

A: Here are some tips for managing credit card debt:

Always read the fine print on credit card agreements to understand the terms and conditions.
Consider using a credit card with a 0% APR promotional period to save on interest charges.
Make multiple payments during the promotional period to minimize interest charges.
Pay off your balance in full before the promotional period ends to avoid interest charges.
Consider consolidating your debt into a lower-interest loan or credit card.

Q: What are some resources for learning more about credit card APR and compounding interest?

A: Here are some resources for learning more about credit card APR and compounding interest:

Federal Reserve. (2022). Credit Card Interest Rates.
Consumer Financial Protection Bureau. (2022). Credit Cards.
Investopedia. (2022). Compounding Interest.
Credit Karma. (2022). Credit Card APR and Compounding Interest.
NerdWallet. (2022). Credit Card APR and Compounding Interest.