It doesn’t take a genius to know that compound interest is a pretty remarkable thing. When your interest earns interest… and then earns some more, it can make for some large numbers over a long period of time. That part isn’t so difficult to understand even though plenty of people have written about it.

So why did I make a video about the “true power” of compound interest? Watch.

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Josh Chan, a student at Stanford University, sent me a video he submitted to Stanford FCU’s video scholarship contest. It’s a superbly done stop-motion video that explains how saving a penny a day can yield you hundreds of dollars after only a short while. I was impressed by the stop motion (I imagine this took a lot of work) and the fact that Josh is financially savvy enough to recognize the value of compounding interest while in college. I wish I was that financially cognizant at his age!

Check out the video:

Contest details

The winner of the contest will be based on the number of votes he or she gets so if you have a moment, register and vote for his video. You can vote once a day until the end of September. If you’re as impressed as I am by the video, I know you’ll join me in voting for him.

What did you think?

Near the end of May, the FDIC Board of Directors approved a rule that capped the interest rate “less than well capitalized institutions” could offer. For quite some time they listed weekly national rates. It was only until last month did they institute rate caps, which are defined as 75 basis points above the national rate. The national rate is just the simple average of rates paid by all insured depository institutions and branches for which data are available.” If a region has a much higher prevailing rate, then banks in that region will be allowed to use local averages plus 75 basis points as the rate cap. This rule wouldn’t go into effect until January 1, 2010.

The idea is that a bank that isn’t well capitalized will be in dire need of some liquidity and boosting your rates is a great way to increase deposits but put you in a difficult spot down the road. When Washington Mutual offered 5% APY certificates of deposit, everyone knew that it was a play for deposits. This rule would make that impossible.

What do you think? Is this a good idea or a bad idea? Do you think that the government is overstepping?

Incidentally, the current rate cap, effective 6/8/2009, on a savings account is 0.96% and a 12 month CD is 1.98% APY. Those are some pretty sad rates.

Debt.

Some see it as a tool to be used to help them improve their financial situation. Some see it as a temptation to get more than you should be allowed to. And some see it was an insidious monster lurking around the corner, waiting for you to slip and make a mistake. Some see it as something the never want to touch.

Today we’re not going to talk about any of that stuff. Today I want to share with you some “fun facts” about debt that you might find useful at your next trivia night!

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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!

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.

Mortgages

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):

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

Legend:

• 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.

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!)

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.

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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 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.