# 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%

|     |   Comment #1
Thank you for a very clear explanation.
|     |   Comment #2
Thanks much for explaining in detail.
|     |   Comment #3
I've passed actuarial exams, and I think you have done an exceptional job of explaining this very clearly for the unexperienced folks out there. Great job!
|     |   Comment #5
Great stuff, even though I've never heard of this website before; thanks
|     |   Comment #8
OMG! A whole week in class and you summed it up in 5 minutes. Great job!!
|     |   Comment #10
Thanks
|     |   Comment #12
Understanding these terms are not only helpful for profesional knowledge, but they will also be great for personal use. It will help you understand bank documents and conversations and letters with/from banks, HRMC and accountants.
|     |   Comment #17
Wonderful explanation, just...
When 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.
|     |   Comment #18
Do you have a calculator for a % APY with taking interest monthly?  How much it decreases the interest APY?  EX 2.15% APY taking interest monthly.
|     |   Comment #19
Impressive and well explained!
|     |   Comment #20
Very clear. Thank you.
|     |   Comment #21
you made this very easy to comprehend...thank you
|     |   Comment #22
Thanks for the clear explanation :)
|     |   Comment #23
If you buy a CD with a 5 year term paying 1.6% ...do you get 1 payment at the end of 5 years of approximately \$3000.00  or do you get 1.6% for each of the years till you get to 5 years?
|     |   Comment #24
Depends upon how and when paid, e.g. some accrue/calculate daily but pay/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.
|     |   Comment #25
All I would like to find out in the simplest explanation is what pays the most \$, is it compounding daily, weekly, monthly or annually
?
|     |   Comment #26
A simple explanation to your question is that the one that pays the highest \$ is the one that pays the highest annual percentage yield (APY) regardless of the frequency of the compounding.
|     |   Comment #48
OK. So here 3 years later I see a bank offering 1.35%, WITH an ASTERISK * .... * "* Interest will be paid on the entire account balance based on the interest rate and APY in effect that day for the balance tier associated with the end-of-day account balance." That stumps me.
|     |   Comment #28
Yes. Thank you.
|     |   Comment #29
This! was a "blessing"! Thank you so much!
|     |   Comment #30
Thank you this was very easy to understand
|     |   Comment #33
what would be the difference on \$15,000.00 at 0.90% and 0.95& for one year
|     |   Comment #34
.90% apy versus .95% apy on 1 Year \$15K.
In 1 year, uou get \$7.50 more in interest for the .95% apy rate on \$15K.
|     |   Comment #36
I'm confused?????I
|     |   Comment #37
Are you sure?
|     |   Comment #40
I plan opening a CD account with Bank Popular Direct. The bank offers 1 year CD with interest rate 1.242% and corresponding APY 1.28%; 2 year CD with interest rate 1.44% and APY 1.52%; 3 year CD - 1.587% interest rate and 1.65% APY. Interest compounds daily.
https://www.populardirect.com/products/cd/cd-36
Can you explain how they calculated these APY's?
|     |   Comment #42
I think everyone should put their money in their mattress, if they can't come up with better rates than are now out there. Banks forget, its our money they use to finance their business.
|     |   Comment #111
Or just put it in a checking account where it gets no interests....
|     |   Comment #119
So get nothing or get at least 1%. Makes sense.
|     |   Comment #120
Or invest in stocks and bonds and **** ahh.. depends on how dedicated you are to learning the game... Little by little.. but I still haven't come to that yet
|     |   Comment #43
Thanks for simple explaination
|     |   Comment #44
If a bank rate has a 2.00% APY checking account, how do I calculate how much interest I earn each month (or each day)? What might that Excel formula be?

I'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!
|     |   Comment #45
It depends on the bank's formula, which is based on policies that can and often do fluctuate. Simple or compounded interest, daily or monthly average balance, limits and a payment schedule are all in the bowels of the code. Check your statements for a few months and reverse engineer.
|     |   Comment #47
Thank you so much for this! Looking at CD and IRA rates on Patelco's websites, and I was just lost lol. Superb job!
|     |   Comment #52
What is meant when the APY is states for 13 months?
|     |   Comment #54
#52
Interest COMPOUNDED over 13 months then reported as a yearly average.
|     |   Comment #53
rates are confusing. what is higher .45 or 1.55?
|     |   Comment #112
Use some math skills. 0.45 0.xx.
|     |   Comment #55
So happy to have found this site but I'm still a little challenged on best way to go. I do understand that a money market gives me immediate access without penalty if I withdraw/close the account at any time and a 12month CD locks my money in for the year because withdrawing or cashing in before the year end would result in penalty and probably losing any interest accrued. However the compounded monthly on a money market seems better than a flat interest rate on a CD. Question: how much interest would I get after one year on a \$25,000.00 money market 1.60% compounded monthly in comparison to a \$25,000.00 12 month CD APY 2.0%.
|     |   Comment #56
I figured it out. Thank you. No need to respond. Thank you
|     |   Comment #65
If I am comparing the APY (not the APR) of two banks on a \$20K 1 year CD and the rates are:
Bank #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?
|     |   Comment #66
If I have \$375,000 in a regular savings account paying 1.8%, compounded quarterly, will I get \$1,687.50 added to my account at the end of three months?
|     |   Comment #73
Very clear explanation. Thank you!
|     |   Comment #74
Great Job!! Got it, get it, good.... ??
|     |   Comment #104
Get it, got it, good. Get it right.
|     |   Comment #75
Thank you for posting this the way you did. It makes it much clearer to understand.
One question though, is the Blended APY calculation based on Monthly or Quarterly Compounding?
|     |   Comment #76
i may be wrong but i think it is based on daily or weekly
|     |   Comment #77
Daily calculations with monthly compounding?
|     |   Comment #78
Do you know If I Invest for example \$1000 at 2.3% one year term versus 2.5% for 18 month knowingly the interest rate will go up every year by 0.25% every year once a year. after 3 years which scenario make more interest ?
|     |   Comment #79
yes after 2 ears
|     |   Comment #80
thank u cassie, hard 2 no
|     |   Comment #82
Citibank is offering 2.00% interest rate for three months and an APY of 0.57% when opening a Citigold checking account. If I deposit \$10,000, then will I receive \$300 after three months?
|     |   Comment #83
Great APY explanation.

Can anybody give me info on Capital Bank (Florida) owned a banking group in Tenn. Exellent, Good, Average or STAY AWAY will do! Thanks!
|     |   Comment #84
I have found that many offers are secretly blended, meaning that they reserve the right to change the rate and effectively do so and a tiered amount is only from a base amount to even earn. The banks always seem to come up with new tricks to over one another. It should be illegal. How is it fair still that forever banks were paying under .25 APR on savings/MMA's and still pulled these types of things. Ok, banks do not have to share how they formulate your monthly interest either-this should be mandatory by all banks and enforced by the gov't.
|     |   Comment #86
Why here are talking about 5% APY when this is what the bank of America offers in a CD account. 0.07% annual percentage yield (APY) on all balances1
|     |   Comment #87
Just want to double-check...since I am comparing the APY between high yield savings accounts, then I can ignore whether the underlying interest date is compounded daily or monthly, concur? So an account with 2.35% APY based on interest compounded daily will yield the same long term savings as an account with 2.35% APY based on interest compounded monthly, right?
|     |   Comment #88
typo: date = rate
|     |   Comment #91
People actually went to school for these answers? This is far basic too basic for the item I was looking for. save 10k and use google my god.
|     |   Comment #92
10k lol what kind of school is that?
|     |   Comment #93
Four decades ago, I finished my university studies and the total four year tuition cost was \$10,900. Now the annual tuition is over \$50,000 putting the four year cost at over \$200,000. How times have changed.
|     |   Comment #94
One minor correction. The formula is not:-
APY = (1 + InterestRate / CompoundingCycles)^CompoundingCycles - 1
APY = { [ 1 + (InterestRate / Compounding Cycles) ] ^Compounding Cycles } - 1
I've used different types of brackets to illustrate the point.
|     |   Comment #107
Actually, Joe, they're the same based on order of precedence. (You can see for yourself by typing both formula's you have written there into a spreadsheet and you'll get the same results.)

The 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.
|     |   Comment #95
My problem is probably more simple. My Credit Union shows an interest rate of 0.03% and another on this extensive list shows 2.40%. Both written as a decimal AND a percent! Which is it? When I studied decimals and %s, about 65 years ago, to convert a % to a decimal you moved the decimal point 2 places to the LEFT and removed the % sign. Thus the 0.03% is 0.003 percent interest (terrible) and 2.40% is 0.0245 percent interest (fairly good). Are they all mis-writing and 0.03% actually means 3% and therefore the 2.40% is actually a phenomenal 240%? What am I missing here? Or is it the financial ins****ions error? Sign on folks, tell if I am correct or gotten a heck of lot older and am 'losing it?
Makes 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 ! ! !
|     |   Comment #103
(insert insightful comment here) I'm from the future.
|     |   Comment #105
Great explanation!
|     |   Comment #110
I want to know why my bank offers higher APY on savings accounts than they do with IRAs. Wouldn't that mean it's better to save for retirement with a savings account instead of an IRA?
|     |   Comment #114
Could be. Depends, what type of IRA are they offering?

Keep 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.
|     |   Comment #115
Thank you for a very clear explanation. super!
|     |   Comment #121
Would this be compatible with the rule of 72?.?.?. The formula that tells you how long it will take your interest rate to double your money?.?.?. Because on even a 3% interest rate it appears to take 24 years to do so.
|     |   Comment #122
I appreciate the breakdown of the APY acronym as well as all of the other technologies.
|     |   Comment #124
What is my account balance at the time

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