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# Understanding Interest Rate and APY

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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%

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Comment #1 by Anonymous posted on
Thank you for a very clear explanation.

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Comment #2 by Anonymous posted on
Thanks much for explaining in detail.

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Comment #3 by Craig (anonymous) posted on
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!

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Comment #4 by siva (anonymous) posted on
Thanks for the  wonderful document.

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Comment #5 by Bob (anonymous) posted on
Great stuff, even though I've never heard of this website before; thanks

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Comment #6 by Anonymous posted on
Thanks for the info but I do it the lazy way.  I find most banks have the interest rate and the APY posted or can give it to me over the phone.  Then all I have to do is run them both on my handy calculator and find out the difference and make my decision on which one I will go with.

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Comment #8 by Anonymous posted on
OMG! A whole week in class and you summed it up in 5 minutes. Great job!!

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Comment #10 by Anonymous posted on
Thanks

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Comment #12 by Friday Friday (anonymous) posted on
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.

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Comment #17 by Anon (anonymous) posted on
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.

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Comment #18 by Anonymous posted on
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.

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Comment #19 by John P. (anonymous) posted on
Impressive and well explained!

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Comment #20 by Anonymous posted on
Very clear. Thank you.

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