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## Annual Percentage Rate Versus Annual Effective Rate – Can You Differentiate?

When a product provider quotes an interest rate, it’s not always immediately clear how much you will pay – or be paid – if you take out the product.

Financial firms like to sell complex products. That way customers don’t know what they’re buying, understand the potential downsides, or realize the true costs, many of which will be skillfully hidden in the small print.

Let’s go through these 2 terms.

**annual percentage rate (APR)**

- Also known as nominal rate or annual simple interest rate
- Does not take into account the effect of intra-year compounding
- Quoted by financial institutions when they lend money, therefore earning interest from customers.
- The main reason is to give customers the impression of low cost of borrowing
- Generally applies to loans, mortgages and credit cards
- The APR is always effectively lower than the quoted AER
- APR to AER conversion mathematical equation: AER = (1+APR/n)^n – 1

__Annual Effective Rate (AER)__

- Also know as Effective Annual Rate (EAR), Annual Percentage Yield (APY) per annum.
- Takes into account the effect of intra-year compounding
- Quoted by the financial institution when customers deposit money, so customers pay interest.
- The main reason is to give the impression that customer deposits earn more interest
- Generally applicable to savings accounts, fixed deposits.
- The AER is always higher than the quoted APR if there is 2 or more intra-year compounding. The only time when AER = APR is when there is no inter-year compounding,
- AER to APR Conversion Mathematical Equation: APR = n[(AER+1)^(1/n) – 1]where n = number of times for intra-year compounding

__APR – A credit card’s annual interest rate__

Let’s say you’re one of those who spend more than you earn and frequently miss your payments, putting yourself in the Tier 3 interest charge bracket of 17.5% per annum.

Say, you have an outstanding balance of $10,000, so you would think (as I did before) that, if I don’t pay a cent for the next 12 months, by 13-months, I would need to pay 117.5. % x 10,000 = $11,750. Or, you think, every month, I will be charged a monthly interest of 17.5% /12 = 1.4583%.

Not so simple. Confused? Consolidate the concept with the example below.

Remember, you receive your credit card statement monthly – your outstanding balance and previously charged interest will be carried forward to the next month. This means, the compounding period is monthly!

In other words, you know very well that, for the first month, the outstanding balance plus interest is $10,145.83. In the second month, 1.4583% interest will be charged on the $10,145.83 brought forward from the first month. See the compounding effect here?

Effectively, once you want to settle the outstanding balance after the 12th month, you will pay more than the advertised interest rate of 17.5% due to compounding, because 17.5% is really the APR!

The actual interest rate you pay is the AER. For an APR of 17.5%, the AER is 18.974%!! See the APR to AER conversion equation above. or in 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 rate and PV = -10,000. Put zero for Pmt. The concept is the same.

So, why did the banks quote you 17.5%?

Simple, because it is the lower number between the two. When you owe money to a bank, the bank needs to give you a disguised impression that you owe less than what you are actually paying. It’s marketing – they’re not actually lying to you, just that it’s not the whole truth. You have nothing to blame but your own ignorance. Different countries have different rules and regulations to combat some of the unethical activities around quotation rates that have arisen in the past; However, there is no better insulator against these measures than proper financial knowledge. If you know of any banks that quote AER instead of APR for credit card interest, let me know – I’m sure their credit card products wouldn’t sell well even if they were telling customers the truth!

__AER – Truth Revealed! Fixed Deposit Annual Interest Rate__

Assume $30,000 held as a fixed deposit for a period of 1 month with interest at 3 percent per annum. The principal and interest will be credited to the savings account after maturity.

Your accrued interest will be $73.97 by the end of the month

You asked why? If it is 3% per annum, the monthly interest rate based on the principal of $30,000 should be (3/12)% x 30,000 = RM 75.

The truth here is that the 3% annual rate is actually the AER, which is your total return based on $30,000 if your monthly earnings interest is added to your initial principal, and the total is carried forward to the next month for 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 the quoted 3% per year **If and only if** Your monthly interest is added to the principal and carried forward to subsequent months for 12 months. If the monthly interest is deposited into your savings account every month for 12 months you will not actually get 3% per year on your principal amount.

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 887.64 over 30,000.

In this scenario, it is in the bank’s best interest to quote you the AER instead of the APR. They know that when you are a borrower, you are looking for the highest interest rate possible to entice you.

Feeling cheated? yes Questionable marketing? be double Why can’t they present the real reality? How many non-personal-finance-savvy people know about this?

Here is a quote I read somewhere:

*Other industries care about loyal customers. Banks do the opposite; Offering great deals to new customers while ignoring their existing customers, the longer you’ve banked with them.*

**AER and EAR are essentially synonymous. EAR is the term adopted for overdraft calculation.*

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