When a product vendor quotes an interest rate, it is not always immediately apparent how much you will pay, or be paid, if you recall the product.
Financial companies love to sell complex products. That way, customers won’t know what they’re buying, won’t understand potential downside risks, or realize the real costs, many of which will be hidden by experts in the fine print.
Let’s go to these 2 terms.
Annual percentage rate (APR)
- Also known as the nominal rate or simple annual interest rate
- Does not take into account the effect of intra-annual capitalization
- Quoted by the financial institution when they lend money, therefore, they get interest from the clients.
- The main reason is to give customers the impression that it costs less to borrow.
- Typically applicable to loans, mortgages, and credit cards
- The APR is always effectively lower than the quoted APR
- Mathematical conversion equation from APR to AER: AER = (1 + APR / n) ^ n – 1
Annual effective rate (APR)
- Also known as Annual Effective Rate (EAR), Annual Percentage Yield (APY) per year
- It takes into account the effect of intra-annual capitalization
- Quoted by the financial institution when clients deposit money and therefore pay interest to clients.
- The main reason is to give clients the impression that client deposits earn more interest.
- Normally applicable to savings accounts, fixed deposits.
- The APR is always higher than the quoted APR if there are 2 or more intra-annual capitalizations. The only time that AER = APR is when there is no intra-annual compounding,
- Mathematical conversion equation from AER to APR: APR = n[(AER+1)^(1/n) – 1], where n = number of times for intra-annual compounding
APR: the actual cost of the annual credit card interest rate
Suppose you are one of those who consistently spend more than you earn and frequently miss the payment, which is placed at interest rate level 3 of 17.5% per year.
Suppose you have an outstanding balance of $ 10,000, so you would think (I did before) that even if I don’t pay a single penny for the next 12 months, by the thirteenth month, you would have to pay 117.5% x 10,000 = $ 11,750. Or do you think that every month I will be charged a monthly interest of 17.5% / 12 = 1.4583%
It is not so simple. Confused? Let’s consolidate the concept with an example below.
Remember, you receive your credit card statement monthly; Your outstanding balance plus previously incurred interest will carry over to the following month. That means the compounding period is monthly.
In other words, as you well know, during the first month, the outstanding balance plus interest incurred is $ 10,145.83. In the second month, interest of 1.4583% will be charged on $ 10,145.83 advanced of the first month. Do you see the impact of compounding here?
Sure enough, once you want to pay off the outstanding balance after month 12, you will pay MORE than the advertised interest rate of 17.5% due to compounding, because 17.5% is really the APR!
The real interest rate you will pay is the AER. For an APR of 17.5%, the APR is 18.974%! See the APR to AER conversion equation above. Or in a monetary amount, $ 11,897.40 instead of $ 11,750.00
Still don’t believe me? Calculate FV in Excel with the following inputs: nper = 12 months, 0.014583 for rate, and PV = -10,000. Set zero for Pmt. The concept is similar.
So why did the banks quote you 17.5%?
Simple, because it is a smaller number between the two. When you are the bank’s debtor, the bank needs you to give it the disguised impression that you need to pay less than you are actually paying. This is marketing, they are not actually lying to you, it just isn’t the whole truth. You have nothing to blame but your own ignorance. Different countries have different rules and regulations to combat some of the unscrupulous activities surrounding listing fees that have cropped up in the past; however, there is no better insulator against these ruses than proper financial knowledge. If you know of any banks that list AER instead of APR for credit card interest, please let me know – I’m pretty sure your credit card product won’t sell too well even though you’re telling the truth to customers.
AER – The truth revealed! Annual interest rate on fixed deposits
It assumes $ 30,000 placed as a fixed deposit for a period of 1 month, with an annual interest of 3 percent advertised. Principal and interest will be credited to the savings account after maturity.
Your accrued interest would be $ 73.97 at the end of the month
You asked why? If it is 3% per year, the monthly interest rate based on the $ 30,000 principal should be (3/12)% x 30,000 = RM 75.
The truth here is that the 3% APR is actually AER, which is your total return based on $ 30,000 if and only if your earned monthly interest is added to your starting principal and carried over to the next month, for a total of 12 months repeatedly.
Using the FV function in Excel, where nper = 12, i = 0.00246625 and PV = -30,000, you get FV = 30,900.00. You earn an interest of RM 300, which is 3% of the principal.
In other words, you only earn 3% quoted per year If and only if Your monthly interest is added to the principal and carried over to subsequent months for 12 months.
Example, 73.97 x 12 = 887.64. This is only 2.959% of 30,000!
Now using the AER to APR conversion formula above, you get APR = 2.959%, which is exactly 887.64 over 30,000.
In this scenario, the best thing for the bank is to quote you the AER, rather than the APR. They know that when you are the lender, you are looking for the highest possible interest rate to attract you.
Do you feel cheated? Yes. Dubious Marketing? Double yes. Why can’t they just present the facts as they are? How many non-personal finance savvy people know about this?
Here is a quote I read somewhere:
Other industries take care of loyal customers. Banks do the opposite; rewarding new clients with the best offers and neglecting existing ones, regardless of how long you’ve worked with them.
* AER and EAR are essentially synonymous. EAR is an adopted term for calculating overdrafts.