BVC #6 – Compounding Interest, APR & APY [VIDEO]

I received an email earlier this week from Tomas, asking what daily compounding meant, and I thought it would best be answered with a video post. The video discusses, in very basic terms, what compounding is as well as two common acronyms you see when talking interest rates: APR and APY.

I created an APR to APY (and back) Calculator a while back and it makes it easy to compute the two.

Please let me know what you think!


How To Calculate Blended Interest Rates

A blended interest rate is an interest rate over an amount where parts of that amount are charged, or earning, different interest rates. Blended interest rates are useful in making important comparisons between different offerings such as mortgages or high yield savings accounts.

With mortgages, the math is simple. You’re calculating the rate based on two separate sums. With a bank, it’s slightly more complicated because you are often accruing interest at one rate for part of the year and then accruing it at another rate for the rest of the year. We’ll explain both.


In the home mortgage example, let’s say you have the choice of getting one loan at $100,000 for 6.00% APY or two loans – one at $80,000 for 5.75% APY and one at $20,000 for 6.50% APY. Which is better? In order to make the comparison, you need to calculate the blended interest rate. Fortunately, it’s an easy calculation.

Take each amount and multiply it by the interest rate. Then add all those numbers together and divide by the total amount. In the above example, that would be:

($80,000 x 0.0575 + $20,000 x 0.065) / $100,000 = 0.0590

The blended rate is 5.9%. It is better to get the two loans.

Mortgages Blended Rate Calculator:
Of course I couldn’t leave you hanging without an easy way to calculate this (no commas or dollar signs please):

First Loan: Amount: , Interest Rate: %
Second Loan: Amount: , Interest Rate: %
Third Loan: Amount: , Interest Rate: %
The blended rate is: %

NOTE: You can also use the above calculator to figure out your blended rate of return on multiple investments with different interest rates, it’s the same equation whether you are earning or paying interest.

Bank Interest

Now we get to the example of one sum accruing interest at one rate for part of the year and at another rate for the rest of the year. This is common if your bank offers a promotional rate for new account holders. Everbank is good example – they offer 4.01% APY for the first three months, then 3.21% APY thereafter.

The first step is determining the APR of both rates. Assuming a monthly period, the APR – APY Calculator tells us that the rates are 3.93% APR and 3.16% APR. Dividing each by twelve, we learn that for the first three months your balance will increase by 0.3792% and then increase by 0.2942% thereafter. The blended rate is:

= ( (1+r1/tp)^r1p x (1+r2/tp)^r2p ) – 1
= ( (1.003275)^3 x (1.002633)^9 ) – 1
= ( 1.00985721200 x 1.0239481162 ) – 1
= ( 1.0340414 ) – 1
= 3.40% APY


  • tp is the total number of periods, in our case it was 12,
  • r1 is the first period’s interest rate (APR),
  • r1p is the number of periods you get that promotional interest rate,
  • r2 is the second period’s interest rate (APR),
  • r2p is the number of periods you get that second interest rate (we limit it to 12 months to calculate APY).

To makes things simple, here’s a quick and dirty blended interest rate calculator.

First Period: Interest Rate: % Periods:
Second Period: Interest Rate: % Periods:
The blended rate is: %


APR to APY (And Back!) Calculator

The difference between APR and APY is pretty important to understand (but not difficult to understand) but the math can be a pain. Enter: The APR to APY (and back!) Calculator!.

It’s fairly straight forward, enter in an APR or an APY, confirm the number of compounding periods, and click on the button you want to do. The only limitation in the calculator is that it won’t do continuous compounding. You can just put some large number and that’ll be good enough because its rounded to two decimal points anyway. Another point to confirm is whether “daily compounding” is 360 periods a year or 365 periods, banks may use either one (it won’t matter which one you use because of how the calculator is rounding, it’ll give you the same answer).

APR to APY Calculator (and back!)

Annual Percentage
Rate (APR)
Annual Percentage
Yield (APY)
APR: % APY: %


Converting APR to APY, What’s The Difference?

If you’ve ever seen any interest rates, chances are you’ve seen the tandem of APR and APY splashed across brochures, flyers, banners, and computer screens. If you didn’t know what the difference was, as I didn’t when I first started reading about this stuff, I’ll give you the quick explanation.

  • APR stands for Annual Percentage Rate.
  • APY stands for Annual Percentage Yield.

What’s the difference between APR and APY?

It’s in how they account for compounding. APR doesn’t consider compounding and APY does, meaning APY will almost always be a slightly higher number.

(Click to continue reading…)


Predicting Federal Reserve Rate Changes

Do you ever read the news or watch television and wonder what those speakers mean when they say “the market predicts the Fed will [increase rates/cut rates/do nothing]?” I have.

What they are referring to is the federal funds futures market where traders buy and sell options contracts linked to the federal funds rate. Unlike other options, where an actual asset could be delivered (an oil futures contract is actually a contract to buy or sell oil at a future date), the federal funds futures contract is a little different. Rather than butcher the definition, according to the Federal Reserve Bank of Cleveland:

A fed funds futures contract is an interest rate futures; i.e. a futures contract whose value is based on a fixed-income security or interest rate. The underlying interest rate for the fed funds futures contract is the average daily effective federal funds rate for the delivery month. The final settlement price for a contract is 100 minus this average rate.

When the market “predicts” the next Fed action, it’s really what the wisdom of the masses (the fed futures trading masses) believe, based on their trading actions, what the future federal funds rate will be in the delivery month of the option.

Where can you find this information easily? The Federal Reserve Bank of Cleveland’s Fed Funds Rate Predictions page! It’s updated daily and has tons of information (check out the excel spreadsheet you can download).

How can you use this? Outside of fun trivia, one way to take advantage of this is to avoid buying long term CDs if the prediction says the rates will go up and to buy CDs when the rates are going down. While the predictive ability spans only a few meetings in the future, it can give you a better idea if you’re deciding what to do. Of course, since everything is measured in probabilities, anything can happen.


HSBC Direct Interest Rate APY

HSBC Direct just raised their interest rate, leading many of their competitors. By comparison, ING Direct sits at at 1.85% and E*Trade remains at 1.95% (they are three of the five online banks I considered the best online savings accounts).

Is it worth it for you to move your funds from a 3.00% APY interest rate bank account to a 3.50% APY interest rate bank account? No, because the time your funds are in limbo, not earning interest, will make the effort not worth it (unless you have a ton of money). However, the cost to open a new bank account is practically nil and HSBC used to be one the leaders prior to the recent string of Fed interest rate cuts.

Also, this rate is guaranteed through September 15th, which means they can increase or decrease it over the next three+ months. So, use HSBC Direct if you don’t have an account but don’t bother opening one to transfer funds in for this rate.

 Banking, Personal Finance 

Remember Certificates of Deposit During Fed Rate Cuts

If you think interest rates are falling, put some of your savings into a CD. Since last August (2007), the Federal Reserve, haunted by the spectre of a slowing economy, had been hacking and slashing the Federal Funds and Discount rates. During that run, and until just recently, the prevailing attitude on Wall Street was that the Fed was going to continue cutting the rate until the threat of future inflation balanced out the threat of a recession. With this last twenty five basis point cut at the end of April, the prevailing attitude changed. Analysts now believe the Fed will stand pat and potentially even raise rates in the future.

During those rate cuts, all of the high interest online banks dropped their savings account interest rates dramatically. Since January of this year, the interest rate on E*Trade’s online savings account fell from 4.95% to 3.01% (only to increase, just recently, to 3.15%). ING Direct account holders saw their rates fall from 4.10% to their current rate of 3.00%. If you were able to purchase a CD at the prevailing higher yield online savings account rates for even a year, you’d be sitting pretty on those funds right now and that’s why CDs become popular during a falling interest rate environment.

This is where you say: “Jim, I’m not an idiot, I know that if the rates are going lower then I want to lock in good rates.” Yes, you are not an idiot but the point is I didn’t lock in any funds in CDs, except for my laddered emergency fund, because I didn’t recognize that I should have (or at least should have considered it). It wasn’t an error of judgment but one of ignorance.

Everyone knew rates were going to be cut but not everyone realized they should’ve considered putting a little bit away in certificates of deposit. (I can confidently say that because I know I didn’t) So, the next time you think rates are going to stagnate or fall, lock a little away in CDs.


Don’t Rate Chase High Yield Savings Accounts

The Fed just dropped the federal funds rates, a ton of banks recently dropped their high yield rates on their high yield savings accounts, and now you’re thinking about switching banks, right? Well … don’t be tempted. There are two huge reasons why rate chasing is a foolish endeavor:

  • Rates are not guaranteed.
  • You lose interest in the interim.

(Case in point, when I opened an E*Trade account three weeks ago, the rate was 5.05% – it’s only 4.40% now. That’s a drop of 0.65%!)

Rates Aren’t Guaranteed

Just because you signed up for a 5.05% APY savings account at E*Trade doesn’t mean that the rate will stay there for any period of time. These bank accounts aren’t CDs and the rate can drop just as easily as you can transfer your funds. While it’s tempting to swap your bank account for another one with a higher rate, the higher rate might disappear in a few days simply because that bank was slow to update their rates! Some banks anticipated the Fed rate drop and lowered their rates, other banks will wait until after the Fed move to shift their rates, you have no guarantee which one your prospective bank is. Banks can and will lower rates to as low as they are able to get away with so chasing is never as valuable as you think it is.

Interest Lost

When you transfer the funds between two accounts, you lose the interest that would’ve been earned during that time. The transfer usually will take about a week so that’s 1/52th of your interest gone. While that may not seem like a lot, you start moving your funds around every few months and that 1/52th becomes 1/26th, then 1/13th… you get the picture.

So, let’s say you still want to rate chase, is there anything you can do to ensure the rates stick? No, but you can do the next best thing, start analyzing their CD rates and consider putting some funds into those. What I do at ING is ladder my CDs in $500-$1000 increments such that I create a psuedo-liquid situation (click thru for an explanation of CD laddering). The laddering gives me some downside protection against a big rate drop and you should be looking for something like that. For example, right now I have several CDs in the 4.90% to 5.25% range – the ING rate is currently 4.1%.

So if you want to chase, look for banks that will let you take a no-minimum CD with a decent rate so you can give yourself some protection against a drop.

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