When a product provider quotes a personal finance interest rate, it is not always immediately apparent how much you will be paying - or be paid from personal finance perspective if you take out the personal finance product.
Finance firms love selling complex personal finance products. That way non personal finance savvy customers don't know what personal finance products they're buying, won't understand the potential downside risks, or realize the true costs of the aforementioned personal finance products, many of which will be expertly hidden in the small print of the money and finance product brochure.
Let's get to this 2 terms in personal finance.
Annual Percentage Rate (APR)
Also known as nominal rate or simple interest rate per annum in personal finance
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.
Primary reason being to give customers the impression it costs less to borrow
Normally applicable to loans, mortgages and credit cards in personal finance
APR is always effectively lower than the quoted AER in personal finance
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 financial institution when customers deposits money, hence paying interest to customers.
Primary reason being to give customers the impression customer deposits earns more interests in personal finance
Normally applicable to savings accounts, fixed deposits in personal finance.
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 constantly spend 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 outstanding balance of $10,000, so you'll think (I did previously) that, even 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 if you are not savvy in personal finance. Confused with this personal finance concept? Let's solidify this personal finance concept with an example below.
Remember, you get your credit card statement monthly - your outstanding balance plus interest incurred previously will be carried forward to the subsequent month. That means, the compounding period is monthly! Remember this tips in personal finance.
In other words, as you are well aware, for the first month, the outstanding 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? Compounding is another crucial personal finance concept to keep in mind.
Effectively, once you want to settle the balance outstanding 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
Still 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 banks 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 actually paying. This is marketing in personal finance- they are not actually lying to you, just that it's not the whole truth. You have nothing to blame but your own ignorance if you are not personal finance savvy. 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 and sound personal finance literacy. 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 even though they are telling the truth to customers!
AER - Truth Revealed! Fixed Deposits Annual Interest Rate
Assume $30,000 placed as Fixed Deposit 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 actually AER, which is your total return based on $30,000 if and only if your monthly interest earned is added into your initial principal, and gets carried forward to subsequent 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 added to the principal and carried forward to the subsequent months for 12 months.You DO NOT actually 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. This is the trick employed by bank to trick customer who are not educated in personal finance.
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 personal finance quote I read somewhere:
Other industries look after loyal customers. Banks do the reverse; rewarding new customers with the best deals while neglecting their existing ones, regardless of how long you have banked with them.
*AER and EAR are essentially synonymous in personal finance. EAR is a term adopted for overdraft calculation in personal finance.
