Annual Percentage Rate (APR) and effective APR | Finance & Capital Markets | Khan Academy

Summary

This video explains the concept of Annual Percentage Rate (APR) on credit cards, breaking down how the quoted rate of 22.9% doesn’t reflect the real cost due to daily compounding. It demonstrates how a daily periodic rate of 0.06274% actually leads to an effective APR of 25.7%. The video highlights the importance of understanding compounding interest and its long-term effects, urging viewers to avoid carrying credit card balances to minimize interest payments. It stresses that even small differences in APR can have a significant impact, especially when penalties and additional fees are considered.

Takeaways

• 😀 APR (Annual Percentage Rate) is often quoted by credit card companies to advertise the cost of borrowing money on a credit card.
• 😀 The nominal APR may not reflect the true cost of borrowing, especially when compounded interest is involved.
• 😀 The daily periodic rate (DPR) is used to calculate the daily interest charged on your balance, and it is often a small percentage.
• 😀 When you multiply the daily periodic rate (DPR) by 365 days, it gives you the nominal APR, but this is not the full story.
• 😀 Interest on credit cards is compounded daily, meaning interest is charged on both the initial balance and the accumulated interest.
• 😀 To calculate the true, effective APR, you must raise the daily periodic rate to the 365th power, not just multiply it by 365.
• 😀 Using the formula for compounding, the effective APR ends up being higher than the nominal APR. In the example, it went from 22.9% to 25.7%.
• 😀 Even small differences in APR can have a significant impact over time, especially if you carry a balance for a long period.
• 😀 Carrying a balance on a credit card can result in paying much more in interest than you might expect based on the advertised APR.
• 😀 To avoid high interest, it is recommended not to carry balances on credit cards. If you must, understand the true cost by calculating the effective APR.

Q & A

What does APR stand for and why is it important for credit cards?

APR stands for Annual Percentage Rate. It represents the cost of borrowing on a credit card over a year, expressed as a percentage. It's important because it helps consumers understand the interest they will pay on their balance annually.

What is the difference between APR and the daily periodic rate?

APR is the total interest rate for a year, while the daily periodic rate is the interest charged per day. The daily periodic rate is a fraction of the APR, and it is used to calculate daily compounding interest.

How is the daily periodic rate related to the APR?

The daily periodic rate is calculated by dividing the APR by 365 (the number of days in a year). For example, if the APR is 22.9%, the daily periodic rate is 0.06274%.

Why does multiplying the daily periodic rate by 365 not give the true APR?

Multiplying the daily periodic rate by 365 gives a simple approximation of the APR, but it doesn’t account for daily compounding. The correct way to calculate the effective APR is to compound the daily rate over 365 days.

How do you calculate the mathematically correct APR from the daily rate?

To find the true APR, you raise the daily periodic rate (1 + daily rate) to the power of 365 and then subtract 1. This gives the effective APR, which accounts for daily compounding.

What happens when interest compounds daily on a credit card balance?

When interest compounds daily, the interest is calculated on the balance each day, and this new interest is added to the balance, meaning you’re charged interest on the interest, increasing the total amount owed.

What is the difference between the simple APR calculation and the effective APR?

The simple APR calculation assumes interest is not compounded and is just the daily rate multiplied by 365. The effective APR, however, accounts for compounding and is typically higher than the simple APR.

In the example with a daily periodic rate of 0.06274%, what is the effective APR after compounding daily for a year?

In this example, after compounding the daily rate of 0.06274% for 365 days, the effective APR is 25.7%, higher than the simple APR of 22.9%.

Why does the difference between the simple and effective APR matter?

Even a small difference between the simple and effective APR can have a significant financial impact, especially if you carry a balance over time. The compound interest accumulates, making the total cost of borrowing higher than initially anticipated.

What advice does the video provide about carrying balances on credit cards?

The video advises against carrying balances on credit cards due to the high-interest rates, which can lead to paying interest on purchases made years ago. If you must carry a balance, be sure to understand the full cost, including the effective APR.