Today, we will discuss the Annual Percentage Rate (APR). We will also check the tool that allows you to calculate it easily and help you in making your decision as well. This may be a bit complicated but don’t be intimidated, as we’ll break it all down and explain everything step by step.
Annual Percentage Rate (APR): What Is It?
Let’s start by defining the term APR. There are many different types of interest rates, like nominal interest rate, periodic rate, APY, etc. APR is a certain type of interest rate. Not only does it tell us important things like the cost of a particular loan, but it is also regularly published by all kinds of financial institutions, including banks. It is very useful to be familiar with this ‘metric’.
Why do we calculate APR, why don’t we simply state a nominal interest rate and be done with it? The nominal interest rate is our basic interest rate. We can say a loan with a 5% nominal interest rate is obviously better than a loan with a 7% nominal interest rate. Yes, but it is not enough. While nominal interest rate has its benefits in simplicity, it lacks precision. It doesn’t include the influence of compound interests plus it doesn’t include any potential additional costs.
Let‘s examine this more closely.
1. Nominal interest rate
Very simple to understand, it is the percentage of a certain amount you want to borrow. Let’s say 12% over a year.
2. Periodic rate
We take our nominal rate and divide it by the number of periods. This way we can see the interest rate over our payment period. For example, if we have a nominal interest rate of 12% and we pay our debt monthly over one year, then the payment period is twelve months. In this case, our periodic rate is 12%/12 equals 1%. This means we pay 1% interest per period.
3. Annual Percentage Rate (APR)
We’ll cover the formula in the next segment, but for now, let’s examine the basic idea behind the APR. While Nominal and Periodic rates don’t include any additional fees APR does. In its most basic form, APR is a sum of the nominal interest rate and any additional charges of a loan. Of course, everything is expressed as a percentage of the principal amount. This way APR tells us a more realistic interest by eliminating any ‘hidden costs’ that may come with the loan.
So let’s say we borrow $10,000 with an interest rate of 10% and with a 10 years term. In this case our loan costs $1,000 per year (10% of $10,000). In order to calculate APR, we’ll need to add any additional costs to this. For example, let’s assume bank fees of $500. Across a 10 year period, this is $50 per year ($500 divided by 10 years). This $50 is actually 0.5% of the loan amount (50 divided by 10,000 equals 0.005). Multiply this by 100 and we get a half percent, 0.5%.
APR in this case is a 10% nominal rate plus this 0.5% which equals 10.5%. This would be a better estimation of the loan cost than the simple nominal rate since it includes a $500 fee. We need to pay that fee as well.
APR formula
For the purpose of this text, we’ll use the following formula.
APR = (((Principal x Rate x Periods) / 100 + Additional Charges) / Principal x Periods) x 100, or
Let’s see what the parameters are in this formula.
A – This is our principal, the amount of money we want to borrow. Loan amount if you will.
r – Our nominal interest rate.
F – Our fees and any other additional charges.
n – This is our number of periods. If we pay our debt monthly for two years n would be 24 months.
Now let’s put this into action with a simple example. Let’s assume we want to borrow $1,000, our nominal interest rate is 5%, and we repay our loan monthly for 12 months. We will also assume a $100 additional cost, for example, bank fees. In our example, we have the following values:
A = 1,000
r = 0.05
n = 12
F = 100
By putting all this in our formula, we get:
We can clearly see that APR=5.83% is higher than r=5%. This is because APR takes into account all additional costs. That is why it is a better metric to approximate the true cost of a loan.
APR Calculator: How Does It Work?
Now, let’s check a more realistic example that we are going to calculate using the APR calculator. Let’s suppose we are considering taking a loan of $10,000. Our nominal interest rate is 6% on a yearly basis. The bank has additional charges and fees summed at $1,000. Let’s say that the period is 10 years but we repay our debt every six months. This means two installments every year which gives us 20 as our number of periods.
Feeding all of these parameters to our calculator gives us the result of 6.5%. Again, we can immediately see that the annual percentage rate is higher than the nominal percentage rate. While you may think it is not too much, only a half percent, who cares. For small loans, this may be true, but if we are talking huge sums then even the small differences make a big impact on how much we pay.
We can also check annualized APR. For this example, we have ten years as our payment period. Dividing our APR of 6.5% by 10 we get 0.65%. This means we have a yearly average APR of 0.65%.
Conclusion
While understanding APR is certainly a good thing you should be aware of its disadvantages. We mentioned earlier that the nominal interest rate doesn’t include additional costs as well as the influence of compound interests. APR, as we saw, does include additional charges, but it doesn’t include the effect of compounding interest. For this, we may use Annual Percentage Yield or APY. APY tends to be higher (and often more accurate) than APR, especially at a higher interest rate.
Also, various financial institutions will use different types of fees in their APR calculations. Be aware of that as well before making your decision. The bottom line is to pay attention to APY as well as APR, especially when you’re considering mortgages and credit cards. Also, make sure to ask about what fees are included or not included in the APR.