# How to Calculate Annual Percentage Rate (APR)

Updated on February 4, 2018 Dez has a master's degree in Applied Mathematics from one of the best universities in the Philippines.

Whenever you want to take out a loan, banks tend to quote rates differently. Bank A might quote a monthly add-on rate, Bank B might quote a yearly rate, while Bank C might quote a daily rate. Depending on where you borrow money from, you need to have a standard way of measuring interest rates so you can easily compare different loans and find the right one for you.

This is where the annual percentage rate (APR) comes in. It provides a standard way to compare the costs of different loans in percentage form.

This hub is all about APR. What APR is, why we use APR, some limitations of APR, and an example of how to calculate the APR.

## Why Use APR?

Remember when you were studying addition in school, your teacher always says do not add "apples" and "oranges" because they are different kinds of fruits. This concept also applies when comparing two different things. Instead of thinking of them "apples" and "oranges," you would do better to think of them as "fruits."

This is what the concept of APR is trying to accomplish. It standardizes the "apples" and "oranges" of percentage rates quoted by banks and turns them into "fruits". This is for the benefit of the borrower because it will help you find one that will suit your needs. In most cases, this means the loan with the lowest APR.

## What is APR?

APR describes the interest rate for the year (annualized), rather than just a monthly or daily rate. If all things are equal (fees, costs, etc.), you want to choose the loan with the lowest APR. The loan with the lowest APR implies that the interest payments the bank charges you over a specified period of time is the least among the other choices.

## How to Calculate APR

There are three different ways to compute APR:

1. Compounding the interest rate for each year without considering any fees;
2. Fees are added to the balance due and the total amount is treated as the basis for finding compound interest rate; and
3. Fees are amortized as a short-term loan.

Suppose you are entering into a loan of P1,000 with 4% monthly interest rate and a P100 processing fee to be paid at the end of 1 month. Here are the computations for each way of computing APR:

1. With 100% representing the principal, the compounded interest rate for each year without fees is (1 + 0.04)12 - 1 = (1.04)12 - 1 = 0.6010 or 60.10%;
2. Adding the fee to the balance, we get P1,000 + P100 = P1,100. Taking the fraction of P100 to P1,100, we get 1 / 11 = 0.0909. So to find the compounded interest rate, we get (1.04 + 0.0909)12 - 1 = (1.13)12 - 1 = 3.3345 or 333.45%; and
3. The third method involves adding the fees in the timeline you create when finding the time value of money. This is how it would look like: Each tick in the graph represents 1 period in time (whether it be day, month, year). | Source

The fee was subtracted from the balance. Then to find the APR, you just plug in the values for the formula of finding the time value of money.

## Formula for Present Value With Annuity

with PMT = payments to be made for each period; i = annual interest rate; m = no. of periods per year; and n = no. of years.

## Limitations of APR

In the real world, not all things are equal. There are other fees to consider whenever you want to take out a loan. For example, on a mortgage loan, there might be insurance fees, processing fees, and other discounts you are given by the broker. Because of these factors, the APR's calculated might not be accurate.

The value of these extra benefits will also vary for different people. Say for example, my house gets flooded during a strong typhoon. I would want to get insurance to get my money back when flood water ruins my furniture. But if my house never gets flooded, I would just be wasting my money getting insurance for something that never happens.

So whenever you want to enter into a loan, make sure you look at every single charge or expense related to the loan so you can ascertain for yourself whether or not you are getting a good deal.

Also, consider the timeline of the loan. Single up-front charges can drive up the cost of the loan, even though the calculation for the APR might assume they are spread over time, which would make the APR look lower than it really is. While balloon payments or any other payment schemes can be taken into account when calculating for APR, most online calculators cannot do this. So it pays to know how to calculate APR manually.

## Example on How to Calculate APR

Suppose we are entering into a loan for P100,000 to be paid in 6 months time. Monthly payment was calculated to be P17,970. The monthly add-on rate is 1.30%. There is a processing fee of P1,300 to enter into the loan.

Let us do each method of calculating for APR.

1. (1 + 0.013)12 - 1= (1.013)12 - 1 = 1.1677 - 1 = 16.77%.
2. P100,000 + P1,300 = P101,300. Taking the fee as a fraction of this new balance, we get, P1,300 / P101,300 = 0.01283. Thus, (1.013 + 0.01283)12 - 1 = 35.80%.
3. Because P1,300 is an up-front fee, the present value at time 0 is P100,000 - P1,300 = P98,700; PMT = P17,970; n = 1/2 (for half a year); m = 12 months. So using the formula for present value of annuity and solving for i, we get:

Unfortunately, there is no possible way to isolate i. If you have a regular calculator, you will have to guess and check for i. Raising the interest rate if the PV(Annuity) is lower than 98,700, and lowering the interest rate if the PV(Annuity) is higher than 98,700.

If you want to find i more easily, you can use Microsoft Excel's formula or a financial calculator. Using Excel, input =Rate(6, -17970, 98700) to get 2.5851%. This is the monthly rate or i/12. To get APR, we need to multiply the rate by 12: 2.5851% * 12 = 31.02%.

## Conclusion

While the third method might be more complicated, I find that it is the best method available since it takes into account when fees are paid, the periods when the monthly payments are made, and any other factors that might affect APR.

So when calculating for APR, just take note that online APR calculators will not be able to take every single cost into account and might give you a wrong value. Just follow the method shown here and plug it into your Microsoft Excel to get a more accurate APR.

Don't forget to read up on any other fees you will incur by taking up the loan, as well as any benefits written in fine print before you sign.