# APR and APY for student loans

Looking for an explanation of what is APR and APY in your student loan applications? Know more about how they are calculated?

Updated by Sharan Kumar on 16th August 2019

Annualized percentage yield or **APY** of a loan is a sort of a calculation that reflects the interest that is earned from the previously accumulated interest. Whereas, annualized percentage return or **APR** for short is a much simpler figure that does not take into account the compound interest that accumulates on a loan.

Hence, there occurs a discrepancy when banks and credit unions use APR and APY for various purposes in their marketing.

## Table of Contents

## Annualized Percentage Rate (APR)

The APR or Annualized Percentage rate is determined by the product of periodic rate, and the number of periods in each year.

**APR = periodic interest rate x total number of periods**

It is very simple to calculate, It gives us an estimate of the rate of interest accumulated over one year. Sadly does not account for the additional sums that might be earned by previous interest payments, which is a process called **compounding**.

**For example:**

A loan that charges the borrower an interest rate of **1.00%** every month. The APR of this specific loan would come out to be **12*1.00%** which is **12.00%** but would be different from a loan that is earning **12.00%** once in 12 months.

Hence, the loan which is compounded monthly will accumulate a much higher interest rate than the loan that is compounded annually. Therefore the two have the same APR because the compound interest is not included here.

In many cases, you can expect to pay a rate that is higher than the APR and is mentioned for the loan or credit account. The more often the loan interest is compounded each year the more the APR will drop short of the real interest rate.

## Annualized Percentage Yield (APY)

Let's consider the APY or annualized percentage yield how it differs from the APR of a loan. Here the loan includes the amount that is earned from compounding the interest.

Mathematically

**APY = (1 + periodic interest rate)^(total number of periods) - 1**

In this theory, a loan that earns **1.00%** interest monthly will yield an APY of about **12.68%**, which is a slightly higher figure that its APR which at the same time would be a solid **12.00%**. It shows the difference between these two, that **APY** does not only calculates the interest rate, but that is also earned by the initial amount of the loan. It also accumulated interest that is taxed again with interest.

The interest that is accumulated every month is being added to the principal of the calculation for interest. Which is then accumulated to the next month, in essence, your interest accumulated also adds value to the interest that is accumulated the next month.

## How do banks use APR and APY?

Different types of banks or credit unions offer different types of credit cards for your loan account. You will find it most often that the interest rate that is used to estimate or describe it is the APR. Whereas, the APY is commonly attached to that where the customer is trying to earn interest as a lender.

**For example:**

Let's take a customer who is adding money in his savings account and cash deposit, this will be described by using the APY in terms of earning potential. Since the customer is seeking to earn the highest possible rates from their money.

The APR has a **lower interest rate** than what is paid for in the end. So, banks often use it to market their products. In which they are looking to pay the least interest possible such as credit card agreements, mortgages and personal loans.

source - pexels.com

According to the Truth in **Lending Act of 1968, **it sets the bar on how lenders like banks and credit unions are allowed to sell their products by marketing them under the guidelines. The law protects its customers by enabling a direct comparison of all their similar products available in the market. To prevent any deceptive or overly complicated presentation of interest rates.

**For example:**

By having all the savings accounts use APY as a common measure to help determine the best for the customers.

## Calculating the differences between APR and APY

The major difference is how the interest is calculated in APR and APY methods. The difference tends to grow far more distinct when the interest that gets compounded is calculated more often.

Let's see the effect of compounding a loan with APY which was marketed with an APR of 10.00%.

Compounded |
APR |
APY |

Yearly |
10.00% | 10.00% |

Semi-Annually |
10.00% | 10.25% |

Quarterly |
10.00% | 10.38% |

%Monthly |
10.00% | 10.47% |

Although the outcome of **0.47%** might seem to be a small amount on its own. Some loans such as home mortgages and others, which involve hundreds of thousands of dollars accumulating interest over a couple of decades.

So based on this we can concur that both the amount and the period of the loan can magnify this effect of compound interest. It can lead it to build a significant force with significant weight on your financial plan.

## Real interest rate taking inflation into context

The compound interest rate adds cost to the loan. The constant effect of inflation acts oppositely, as the currency loses its value over time and more dollars are needed to purchase the same goods or services. The money in a loan tends to lose its value.

source - pexels.com

The effect that inflation has on the interest rate of a loan, is known as the real interest rate. Which is usually anywhere between a lender's marketed interest rate which is named as the nominal rate and the actual rate of inflation.

**Real Interest Rate = Nominal Interest Rate - Inflation Rate**

This nominal interest rate that is mentioned by the lenders can either be an APR or an APY type. where usually the APY types will tend to be slightly more of accurate estimation. If the annual interest rates are estimated to be around **1%** then a **1-year** loan which consists of an APY of **10%** will earn you a real interest rate anywhere around **9%.**

It gives a figure when the lender is profited from the interest on the loan. The purchasing power capacity of the last product in profit decreases due to the inflation in the currency that is in use.

Although through the method mentioned above, one can deduce to a certain extent the real interest rate that one will end up paying.

It is difficult to predict or estimate the future rate of inflation over a loan term. Calculating the real interest rate is useful for the lenders who are determining if the investment that they making is worth taking or if it might return yield to you.