APY for the less advanced
- 1How much do we (really) pay?
- 2How much money do we (really) get?
- 3How much do we pay in relation to borrowed money?
- 4When do we pay?
- 5How often do we pay?
- 6How quickly does the value of money change in time?
APY for the more advanced
- 7How much do we pay per year?
- 8Does the way of loan repayment (fixed or decreasing installments) matter if there is no commission?
- 9Does the way of loan repayment (fixed or decreasing installments) matter if there is commission?
- 10Is APY always higher than nominal annual interest rate??
- 11How many different APY’s can one credit have?
- 12Is APY the same as IRR?
„Interest-free” does not always mean „for free”
0% credit does not have to have a zero APY, which means it is not for free. Even if the nominal interest rate is zero, APY also takes into account other credit-related costs, such as commission or insurance. It is enough to pay a commission for an interest-free credit to make its APY higher than zero.
Let’s assume that you contract a credit of PLN 120 000 for one year to build a house. The cost-estimate is for the same amount of money. The surveyor charged PLN 1000 for assessing the investment. Annual nominal interest rate of your credit is 12%. You pay interest every month, in arrears, while the capital is paid in fixed installments. You pay 5% commission for granting the credit. In order to secure the credit you must insure both the investment (property insurance is 0.15% of the amount of credit per year) and yourself (life assurance is 0.35% of the amount of credit per year). Since the bank offers credit for 80% of the value of the property, it requires that you take out insurance for the missing own contribution (3.5% from PLN 24 000 of own contribution). With all these additional costs, the APY of your credit is 29.59% (which is nearly 2.5 times more than its nominal interest rate).
3635% - this is the APY of the so-called „instant loan”
of PLN 500 lent for 30 days in one of loan companies operating in Poland. This equals the total growth in value of gold since 1970, that is for a period of nearly half a century.
Source: Centre for Economics & Business Research / CoinInvestDirect.The amount of money offered by various banks to you may be identical. However, what really matters is whether this amount is not reduced by any advanced payment required by the bank or own contribution. If this is the case, then the capital offered by the bank is not the same as the capital at your disposal, and the above-mentioned reductions constitute additional cost of credit. Having less money at your disposal, you incur a loss. APY of a credit with such reductions is higher than APY without them.
Infernal tricks
The size of font which one of financial institutions operating in Poland used to provide information on APY was 100 times smaller than the size of font in which the main message of the offer was conveyed. We can compare it to text warnings which take up 30% of the surface on a packet of cigarettes.
The sum of all credit-related costs expressed in PLN informs you of the burden you will have to suffer when servicing it. It does not say anything, though, about the sum of money lent to you. With two different credits you may incur the same total absolute costs (for example PLN 500 per month) in exchange for a totally different sum of borrowed money. APY expresses the total cost of credit as seen in a relative perspective, in relation to the sum of money lent to you. It is lower when you borrow more money for the same cost expressed in monetary units.
„Up front” or „down the hill”?
This depends whether you get or spend the money. If you get it, getting it in advance – that is at the beginning of the period (for example a monthly rent for your flat), you enjoy a ride “down the hill”. The money you get can immediately start working for you. However, if it is you who pays, paying “in advance” is like crawling “up the hill”. Paying “in arrears” – that is at the end of the period – you would spend your money later, which would offer you better opportunities to invest it and facilitate making other due payments.
From the perspective of APY what really matters is how long we have the amount we borrowed. The shorter the time we can use this money, the higher the APY and vice versa. If we can pay later, it’s good news – though the price of credit does not change, it actually becomes cheaper. You take advantage of it, because by paying later you decrease what economists call “opportunity costs”, you will not lose some market opportunities, the necessity to credit other expenses will become less likely and if you have any temporary surplus of cash in your budget, it may earn you interest, even in the same bank which offered you credit.
Small print and loss of literacy
Nearly half of Poles have problems understanding public transport timetables and weather maps. The percentage of those who do not understand credit contract provisions is even higher.
Source: research conducted by Programme for International Student Assessment (PISA) and OECD.The size of APY is affected by the frequency of payments. The less frequent your installments are, the more you can invest and vice versa. APY grows along with the increased frequency of payments (you spend capital faster) and declines with the decreased frequency of payments (slower spending of capital). If you have a credit at 4% annual interest and a possibility of making a deposit of 6% annually, you will quickly realize why it is so important – especially when we talk of large amounts of money.
Financial knowledge of homo oeconomicus: a very compound interest
In July 2009, Bloomberg Businessweek quoted some interesting statistics concerning financial knowledge of Americans. Of particular interest were the results of the Health & Retirement Survey conducted by University of Michigan, in which adult respondents were asked to solve several simple mathematical problems, requiring the calculation of the so-called compound interest. A mere 18% of respondents coped with the task. Similar results were obtained in a world-wide survey conducted by OECD in 2005. The survey showed, for example, that in the Australian market, 67% of respondents declared they knew the concept of compound interest. Unfortunately, this is only declarative, not applied knowledge. When these people were asked to do basic calculations using compound interest, only 28% of them performed them correctly.
Source: B. Steverman, Financial Literacy: The Time is Now; OECDHow compound interest works can be best seen on the example of a deposit, though the mechanism is the same in case of credit, too. If you deposit PLN 100 for a year in a bank which offers you a 10% interest rate (paid only once, at the end of the year), after one year you will have PLN 110 (we do not take into account inflation rate and the so-called Belka tax – tax on deposits). However, if at the same annual interest rate, interest will be calculated more often than once a year (and added to the money you deposited in this bank at the end of the year), after one year you will have more than PLN 110. At a given interest rate of 10%, the more frequently interest is calculated, the more you will have. It also matters whether interest will be added at the beginning of the period (in advance) or at the end (in arrears). Adding interest is known as capitalization. Compound interest is a type of calculating interest taking into account capitalization. The higher the frequency of payments, the higher APY. APY diminishes along with delayed payment date.
Can cheaper credit actually be more expensive?
Try to answer this question by comparing two situations. In both cases you borrow PLN 100. Situation one: nominal annual interest rate is 10.3% and the loan is repaid in one installment after a year, with interests calculated for that period. Situation two: nominal annual interest rate is 10%, the loan is repaid together with interest after a month. In the first situation APY equals the nominal interest rate and is 10.3%, while in the second one – in which the credit seems cheaper – APY is 10.47%. It turns out then, that the credit that seemed cheaper is in fact more expensive. What catches our attention at first in case of credits and loans is their nominal interest rate. Unfortunately, it may be misleading, as it does not take into account – unlike APY – other vital features of credit, which may encourage us to choose more expensive credits and believe they are cheaper.
APY is an annual measure, but it is also used with reference to credits and loans contracted for other periods of time. In such situations we must be very careful when interpreting its size. The APY calculation is constructed in a way which assumes that costs of credit contracted for a month will repeat 12 times, for a quarter – 4 times, etc. That is why when we look at APY, a credit contracted for a month seems more expensive than the one contracted for a quarter, and the latter – more expensive than the annual one (assuming all the other credit parameters are the same). That is why lending companies specializing in short-term credits, argue that they should be obliged to publish APY in a more adequate form for them, that is as MPY (Monthly Percentage Yield). This feature of APY also accounts for the fact that APY of a credit with lower interest rate may be higher than APY of a credit with worse interest rate, but repaid in a longer period of time.
Credit as a product – or who reads product information?
Communicating APY resembles placing information on side effects on the medicine leaflet. It is always provided, though few people read it. That’s our habit – only 21.7% of Poles read information on product packages.
Source: survey conducted by ARC Rynek i Opinia for Nestle.APY of a loan is the same regardless of whether it is repaid in fixed or decreasing installments. Obviously, in case of decreasing installments, the sum of interest is lower, but this is due to the fact that we spend (repay) capital on which interest is paid faster (besides, it is methodologically mistake to sum up undiscounted interest). In case of fixed installments it is the opposite: interest are higher, but this is compensated by the fact that we have capital at our disposal for a longer period of time. The net effect is zero. This is why it does not matter whether we repay the loan in fixed or decreasing installments – its APY is the same as long as there are no other than interest costs involved.
As in a distorting mirror
APY of a loan for PLN 500 for 30 days offered by one of lending companies was nearly 3600 percentage points higher than APY of revolving credit in your bank account, with the same parameters as the above loan, but provided by one of leading universal banks. The scale of difference can be visualized when using the following construction business analogy: it is as if instead of a single family house of 150 m² of usable space we would build a complex of buildings with over 5,500 m². This is the space of one of newly built* modern hotels in Tri-city, with 90 rooms.
Source: “APY will tell you the truth. Especially about instant loans”, wp.pl *As of 1st March 2014The loan on which you pay only interest has the same APY regardless of whether you repay it in fixed or decreasing installments. However, burdening you with additional costs, such as commission, makes APY on the same loan different for two options of repayment (even if the commission is identical in both cases). Moreover, if you decide to choose the method of loan repayment on the basis of the sum of interests (that is, you will choose decreasing installments due to the lower sum of interest for the whole period of crediting), after taking into account the commission you will notice that your choice was wrong. The option which seemed cheaper is in fact more expensive (has higher APY). This is because in the construction of APY each expense (here – additional commission) is referred in each subsequent period of loan repayment to the capital remaining at your disposal. Thus, even if the amount of commission is the same in those to repayment options, in relation to the capital at your disposal the quotient is different.
Infernally unpopular credit
Only 5.1% of all students and PhD students took advantage of a student loan.
The interest rate on student loan is ½ of a current rediscount rate of NBP (Polish National Bank) bills of exchange (which, at present, is 2.75% per annum). As PKO BP SA, one of the banks where you can apply for such a loan, informs, its APY is currently 1.04%, so it is much lower than annual nominal interest rate (3.3%)*. This is so due to favorable distribution of payment for the loan-taker and repayments made by him in time, typical of student loans. In the first years of crediting (during the studies), the loan-taker obtains (in installments) capital from the bank (positive monetary flows). The repayment of the loan and related interest (negative monetary flows) starts not sooner than a few years after finishing studies. Negative flows, therefore, are significantly delayed in time, which is additionally strengthened by discounting.
*As of 1st March 2014Is the contract a pact with the devil?
One in five Poles never reads provisions of the loan or investment contract before they sign it.
Source: Survey conducted by TNS Polska and commissioned by UOKiK in August 2012.Calculation of APY is a search for the solution of a n-th degree polynomial, which has n solutions – equal to the number of changes of direction in monetary flows related to credit during the crediting period. Some monetary flows are positive (payment of resources by the bank) some – negative (repaid installments and other credit-related costs). If the credit is paid out at once (positive flow) and then repaid regularly in installments (negative flows), we observe one change of direction in monetary flows (from plus to minus). Such credit has one APY. However, if the credit is paid out in several parts, each of them being positive flow, between which there are periods of installment repayments (negative flows), then we have more than one change of direction in credit monetary flows and more than one APY.
Devilishly expensive credit
20.18% - this was the average APY of consumer credits in Poland at the end of 2013. Compare it with average APY of consumer credits in Finland, which was 5.27%.
Source: Deutsche Bank reportIRR – internal (not infernal) rate of return – presents profitability of investments over time, while APY describes the cost of financing over time. However, the calculation of both parameters is based on the same principles, and each of them is determined in the same way. To realize that APY is the same as IRR it is enough to compare formulas used for calculating both quantities.