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

When a product provider quotes an interest rate, it is not always closest apparent how much you will be paying – or be paid – if you take out the product.

Finance firms love selling complicate products. That way customers don’t know what they’re buying, won’t understand the possible downside risks, or realize the true costs, many of which will be expertly hidden in the small print.

Let’s get to this 2 terms.

**Annual Percentage Rate (APR)**

- Also known as moderate rate or simple interest rate per annum
- Does not take into account the effect of intra-year compounding
- Quoted by financial institution when they lend out money, hence earning interest from customers.
- dominant reason being to give customers the impression it costs less to borrow
- typically applicable to loans, mortgages and credit cards
- 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 provide (APY) per annum
- Takes into account the effect of intra-year compounding
- Quoted by financial institution when customers deposits money, hence paying interest to customers.
- dominant reason being to give customers the impression customer deposits earns more interests
- typically applicable to savings accounts, fixed deposits.
- AER is always higher than quoted APR if there is 2 or more intra-year compounding. The only time when AER=APR is when there is no intra-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 – The Real Cost of Credit Card Annual Interest Rate__

Assume you are one of those who regularly use more than you earn and frequently misses your payment, putting yourself in Tier 3 interest charge bracket of 17.5% per annum.

Say, you have noticeable balance of $10,000, so you’ll think (I did before) that, already if I don’t pay a single cent for the next 12 months, by the 13-th month, 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 quite that simple. Confused? Let’s solidify the concept with an example below.

Remember, you get your credit card statement monthly – your noticeable balance plus interest incurred before will be carried forward to the later month. That method, the compounding period is monthly!

In other words, as you are well aware, for the first month, the noticeable balance plus interest incurred is $10,145.83. On the second month, the 1.4583% interest will be charged on $10,145.83 brought forward from the first month. See the impact of compounding over here?

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

The actual interest rate you will be paying is the AER. For APR of 17.5%, the AER is 18.974%!! See APR to AER conversion equation above. Or in monetary amount, $11,897.40 instead of $11,750.00

nevertheless don’t believe me? Compute FV in Excel with the following inputs: nper = 12 months, 0.014583 for rate and PV = -10,000. Put zero for Pmt. The concept is similar.

So, why edges quoted you 17.5%?

Simple, because it is a lower number between the two. When you are the bank’s debtor, bank need you give you the disguised impression that you need pay less than you are truly paying. This is marketing – they are not truly 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 in place to combat some of the unscrupulous activity surrounding quoting rates that has arisen in the past; however, there is no better insulator against these ruses than proper financial knowledge. If you know of any bank which quote AER instead of APR for credit card interests, let me know – I am pretty sure their credit cards product would not be selling too well already though they are telling the truth to customers!

__AER – Truth Revealed! Fixed Deposits Annual Interest Rate__

Assume $30,000 placed as Fixed place for period of 1 month, with advertised 3 percent interest per annum. Principal and interest will be credited to savings account after maturity.

Your earned interest would be $73.97 by the end of the month

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

The truth here is that 3% annual rate is truly AER, which is your total return based on $30,000 if and only if your monthly interest earned is additional into your initial principal, and gets carried forward to later month, for a total of 12 months repetitively.

Using FV function in Excel, where nper=12, i=0.00246625 and PV=-30,000, you get FV=30,900.00.You earn interest of RM 300, which is 3% of the principal.

In other words, you only earn the quoted 3% per annum **if and only if** your monthly interest is additional to the principal and carried forward to the later months for 12 months.You DO NOT truly get 3% per annum out of your principal if the monthly interest is credited to your savings account every month for 12 months.

Example, 73.97 x 12 = 887.64. This is only 2.959% of 30,000!

Now using AER to APR conversion formula above, you get APR = 2.959%, which is exactly 887.64 over 30,000.

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

Feeling cheated? Yes. Dubious marketing? Double yes. Why can’t they just present the facts just as it is? How many of non-personal-finance-savvy people know about this?

Here’s a quote I read somewhere:

*Other industries look after loyal customers. edges do the reverse; rewarding new customers with the best deals while neglecting their existing ones, in spite of of how long you have banked with them.*

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

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