# Understanding Interest Rate and APY

Understanding the different terms used to describe interest rates can be confusing at first. Generally you will see the term interest rate mentioned, along with APR or APY, so what’s the difference? Using APR and APY calculations to compare various investments and the real cost of a purchase requires that you understand what each of these terms mean, and how interest is calculated and compounded.

## Interest rate

The “interest rate is the simplest term to understand. It simply means the amount of interest that will be paid on an investment you make; or the amount charged on a loan per year. It may seem that this is all you need to know and when looking at deposit products that pay simple interest, it pretty much is. Interest rates get slightly more confusing to calculate and make sense of when there is compounding involved.

## Simple Interest

Simple interest is just that and is typically used with savings bonds. It means if you invest $1,000 at 5% interest, at the end of the year you will receive a $50 check. At the end of next year you will receive another $50 check. This will happen every year for the length savings bond term. Simple.

## Compounding Interest

The problem is most of us don’t want to receive a small check in the mail each year for the interest we earn. Instead, we want to leave the interest earned in the account and let it grow over time. When the interest earnings are left in the account, the balance of your money grows and the interest is calculated on that total balance.

In this scenario, during the second year you really should earn more than $50 in interest since the bank has $1,050 of your money, instead of just the original $1,000. This act of receiving a larger amount each year due to being paid interest on the prior year’s interest is known as compounding. Here’s a table that shows how your original $1,000 investment would grow over 10 years.

Year |
Starting Balance |
Interest |
Ending Balance |

1 | $1,000 | $50.00 | $1,050.00 |

2 | $1,050.00 | $52.50 | $1,102.50 |

3 | $1,102.50 | $55.13 | $1,157.63 |

4 | $1,157.63 | $57.88 | $1,215.51 |

5 | $1,215.51 | $60.78 | $1,276.29 |

6 | $1,276.29 | $63.81 | $1,340.10 |

7 | $1,340.10 | $67.01 | $1,407.11 |

8 | $1,407.11 | $70.36 | $1,477.47 |

9 | $1,477.47 | $73.87 | $1,551.34 |

10 | $1,551.34 | $77.57 | $1,628.91 |

By year 10 in this example, you are earning $77.57 in interest compared to $50 in the first year. The growth is very gradual at 5%, but with higher returns and longer investment periods the compounding effect is much more dramatic. A retirement account funded with a single $1,000 initial investment, that averages 12% return for 40 years, will earn $9,969.75 in the 40th year alone thanks to compounding interest.

## Compounding Period

In the previous example, interest was paid on the investment once per year, which means it has an annual compounding period. In this case the APY and interest rate paid on the investment are identical. However, most banks offer more frequent compounding periods. Common values are quarterly, monthly, weekly or even daily. In these situations, you will be paid 1/4th of the 5% each quarter, 1/12th of it each month or 1/365th of it each day. So what’s the difference? Isn’t it still 5% a year no matter how you slice it?

No, it’s not. The reason is the same compounding effect that happened each year in the previous example, also starts to happen on a much smaller scale with more frequent compounding periods, which results in better returns. Where earning 5% once per year earned $50 in the previous example, earning 1/12th of 5%, or 0.417% each month will yield you $51.20 thanks to the compounding interest effect taking place on a monthly basis. It may seem like a small difference but this adds up over time.

## APY

What if one bank is offering 5.1% interest compounded annually and another is paying 5.0% interest compounded daily. How do you know which one is better? Without doing a bunch of math every time you want to compare another offer, you really can’t tell. This is where the APY comes in handy.

APY stands for annual percentage yield. It takes into account the interest rate and compounding period to give you a single number that represents how much you will earn from that investment in one year. In the example in the previous section where you earned $51.20 thanks to your account compounding monthly, that account would have an APY of 5.12%, even though the interest rate on it was 5.00%. This gives you a single number that allows you to easily compare one bank’s offerings to another.

APY is similar to APR or Annual Percentage Rate. The difference is APY is used with deposit accounts where you are earning the interest and APR is used to describe the rate you pay on loans. APR also factors in loan fees that must be paid, which is not applicable in APY calculations for deposit accounts.

## Calculating APY

Most banks publish the APY for their accounts just as prominently as the interest rate so it’s rare that you would ever need to calculate it, but I know there are some math junkies out there who want a simpler way than putting together an Excel spreadsheet with a repeating formula. Here’s how you do it.

*APY = (1 + InterestRate / CompoundingCycles) ^{CompoundingCycles} - 1*

To give you an example, with the 5% interest rate, compounding 12 times per year the formula would be:

* APY = (1 + 0.05 / 12) ^{12} - 1 APY = 0.05116 APY = 5.12%*

## Blended APY

Some accounts pay different rates based on how much you have invested, known as tiered rates. For example, you may earn 3% on balances under $10,000 and 4% on balances over $10,000. In most cases if you deposit more than $10,000 you will receive the 4% on the entire balance, but in some cases you will only receive the 4% on the portion of the balanced. This is known as a blended APY.

Banks that offer blended APYs typically list the rate for the higher tier as a range. Instead of just showing 4% in this example, the APY will show 3%-4% because the APY you receive on the entire balance will vary based on how much you deposit. This can make it difficult to compare rates between banks. Is this account better or worse than one that pays 3.5% on your entire balance?

It depends on how much you have invested. If you have $15,000 invested, the first $10,000 will earn 3% and the remaining $5,000 will earn 4% for a average return, or blended APY of 3.33% making the 3.55 flat rate a better deal, but if you plan to invest $50,000, the blended APY jumps to 3.80%. To calculate the blended APY you use the formula.

*Blended Apy = (Amount1 * Rate1 + Amount2 * Rate2) / Total Amount*

For the $15,000 example it would be:

*Blended Apy = ($10,000 * 0.03 + $5,000 * 0.04) / $15,000 Blended Apy = ($300 + $200) / $15,000 Blended Apy = 3.33%*

Anonymous| | Comment #1Anonymous| | Comment #2Craig| | Comment #3siva| | Comment #4Bob| | Comment #5Anonymous| | Comment #6Anonymous| | Comment #8Anonymous| | Comment #10Friday Friday| | Comment #12Anon| | Comment #17When a bank or credit union lists their dividend or interest rate the same as the APY, what does that mean exactly? Like say, for a money market account for $10,000, monthly term, dividend rate of 0.25%, and an APY of 0.25%, what will that amount come to at the end of a year? Would I only receive 0.25% a year, or monthly.

Anonymous| | Comment #18John P.| | Comment #19Anonymous| | Comment #20Anonymous| | Comment #21Anony| | Comment #22mikeM| | Comment #23Anonymous| | Comment #24accrue/calculate dailybutpay/post quarterly...those are the deal terms going in. The apy fluctuates a little depending upon those terms. Ask the issuer of the CD for underlined items.Anonymous| | Comment #25?

Anonymous| | Comment #26konabish| | Comment #48Anonymous| | Comment #28Jen| | Comment #29Anonymous| | Comment #30Anonymous| | Comment #33Anonymous| | Comment #34In 1 year, uou get $7.50 more in interest for the .95% apy rate on $15K.

tergarry| | Comment #36Anonymous| | Comment #37Bob| | Comment #40https://www.populardirect.com/products/cd/cd-36

Can you explain how they calculated these APY's?

watcher| | Comment #42InterestSeeker| | Comment #111Himanshu| | Comment #43mike| | Comment #44I'm trying to create a monthly budget, and knowing that I have money flowing in/out of the checking account each month is something I'd like to work into my formulas. Each month, my balance will be different (cash in cash out), so want to estimate the interest earned each month knowing only the bank APY rate.

Thanks!

We Need Humor| | Comment #45Mr. Thankful| | Comment #47wonedering| | Comment #52anon| | Comment #54Interest COMPOUNDED over 13 months then reported as a yearly average.

confused| | Comment #53InterestSeeker| | Comment #112Chaya| | Comment #55Chaya| | Comment #56pradcliffe| | Comment #65Bank #1 2.% APY, compounded daily.

Bank#2 2.% APY compounded annually

I am going to walk away from either bank at the end of the year with $400.00 in interest. Correct?

Is the same true of a multiple year CD paying the same APY?

Jean| | Comment #66Anonymous| | Comment #73Happy Webster Employee and Customer| | Comment #74Neo| | Comment #104Anonymous| | Comment #75One question though, is the Blended APY calculation based on Monthly or Quarterly Compounding?

motor mouth| | Comment #76Anonymous| | Comment #77MIke 57| | Comment #78cassie| | Comment #79goober| | Comment #80Flounder| | Comment #82Nando| | Comment #83Can anybody give me info on Capital Bank (Florida) owned a banking group in Tenn. Exellent, Good, Average or STAY AWAY will do! Thanks!

METOO| | Comment #84Erik| | Comment #86TheRedOak| | Comment #87TheRedOak| | Comment #88basics| | Comment #91JO Jane| | Comment #92DCGuy| | Comment #93Joe| | Comment #94APY = (1 + InterestRate / CompoundingCycles)^CompoundingCycles - 1

Instead it is:

APY = { [ 1 + (InterestRate / Compounding Cycles) ] ^Compounding Cycles } - 1

I've used different types of brackets to illustrate the point.

GreenDream| | Comment #107The extra enclosing symbols you put around (Interest Rate/Compounding Cycles) is redundant as division takes precedence over addition. and the other added enclosing symbols about everything but the - 1 is also redundant as exponentiation takes precedence over subtraction. (Also note that in Ken's original formula the CompoundingCylces after the ^ was superscripted which already makes it clear the - 1 was not part of the ^CompoundingCycles exponent thus making the added enclosing symbols even more redundant.)

Put another way these two things give the same result:

(1 + InterestRate / CompoundingCycles)

[ 1 + (InterestRate / Compounding Cycles) ]

and these two things also give the same result

()^CompoundingCycles - 1 (note in ken's original CompoundingCycles is superscripted whereas the 1 is not is both were superscripted then you'd have had a case for his formula being wrong.)

{[]^CompoundingCycles} - 1

All they extra enclosing symbols accomplish is to make the precedence that is already in place explicit.

surf1939| | Comment #95Makes me think of when I return something to a retailer and they CREDIT my account. They are NOT Crediting my account, they are DEBITING MY account and are Crediting THEIR account, per my high school, undergraduate and graduate math and/or financial courses. Or have I forgotten something here too? Old Age is only for the Brave ! ! !

Neo| | Comment #103Hsphilic| | Comment #105InterestSeeker| | Comment #110GreenDream| | Comment #114Keep in mind, also, that the tax advantages of IRAs could turn a slightly lower APY into a more attractive proposition than a slightly higher savings account alternative.

venkatakrishnan| | Comment #115