10,000

My math blog just crossed over 10,000 views as of September 3, 2023, so I decided to write some interesting facts about 10,000.

Minnesota, also known as The Land of 10,000 Lakes, actually has 11,842 lakes.

For exercise, many people try to get in 10,000 steps in a day. That's approximately 5 miles or 8 kilometers.

Salmon P. Chase is featured on the U.S. $10,000 note.

There is a "$10,000 rule" which requires banks to report deposits or withdrawals of $10,000 or more of cash.

In English, myriad is used to describe a large number or a countless number of objects. The term is from the ancient Greek word for 10,000, myrias (μυριάς).

Update, 9/29/2023 - a $10,000 note recently sold for $480,000. Link to article.

Readers of this Blog Earned $837 Risk Free

 

(Graphic: Laura Reen on Iconfinder)

Last year, this blog suggested buying United States I Bonds as way to protect savings from inflation. The I Bond series pays interest rates adjusted twice yearly for inflation. Last November, the interest rate was set at 7.12% and in April this year, the rate was adjusted to a 40-year high of 9.62%. Readers who took the advice of this blog and bought the maximum allowed amount of $10,000 earned $837 over the past year. Next month, the rate will be adjusted again. It is anticipated that it will likely be 2 – 3 % lower than the 9.62% rate I Bonds have been earning since April.

 Individual - Buying Series I Savings Bonds (treasurydirect.gov)

For information on the rates, Go to: https://www.treasurydirect.gov/indiv/research/indepth/ibonds/res_ibonds.htm#irate

If you don't have an account already, set one up here: https://www.treasurydirect.gov/RS/UN-AccountCreate.do

What are all those different numbers on U.S. Currency?

 

Every day when you handle currency, you probably pay the most attention to the numbers in the four corners in the front and back which indicate the bill’s denomination. There are other numbers found on currency that we’ll review in this post.

Denomination

The denomination is also spelled out on the front and back. With denominations, five dollars and higher, there will also be field of small cluster of “05”s, “10”s etc. found on either the front or the back. With the five, the cluster is found on the front, left of Lincoln’s head. With the twenty, the cluster is found on the back, left and right of the White House. For those with exception near vision or with the aid of a magnifying glass, the denomination is also microprinted in various locations as a security feature. Some examples of the microprint are in the security thread (can be viewed when held up to light) and other locations depending on the denomination such as “20 USA 20” found between Jackson’s shoulder and the signature of the Treasurer of the United States. Bills of denomination five and higher, have a security watermark. With the five, it is a large 5 on the right-hand side; with the twenty, the watermark is a portrait of Jackson on the right-hand side. The locations of some of these features are shown below.

Serial Number

The serial number of U.S. currency is printed twice on the front. It consists of one or two letters, followed by eight numbers and ending in a final letter. See my prior posts about the eight-digit serial numbers. If the bill has two leading letters, the first letter corresponds to the “series” of the currency – the series is also listed just right of the portrait, near the signature of the Secretary of the Treasury. When the bill’s serial number has only one leading letter, the letter corresponds to one of the twelve Federal Reserve Banks (this would be the second letter on newer bills having serial numbers beginning with two letters). In the example note shown above, the letter N corresponds to the 2017 Series and the letter L corresponds to the 12th Federal Reserve Bank - San Francisco. Older notes would list the bank by name left of the portrait, but newer notes use a common United States Federal Reserve System symbol left without listed the specific bank of the portrait. On the front of the bill, there should also be number printed two to four times that matches the Federal Reserve Bank serial number letter designation – 1 for A, 2 for B, etc. Newer bills, this number is also found with a repeat of the corresponding letter, for instance A1, B2…L12.

 

Plate numbers

Modern currency is not printed one bill at a time, but in sheets of 32 or more. Each note’s position on the sheet is designated a small letter and number. The plate position designation is found on the left-hand side (G3 in the above example). For the sheets of 32, the sheet is divided into four quadrants designated by the numbers 1 through 4 and the position within the quadrant is denoted by the letters A through G. The plates that print the bills are also serialized. Their number is printed on the right-hand side and consists of letters and numbers (FW G 3 in the example). In slightly larger font, the plate position letter designation is repeated in the middle of the plate serial number (G in the example). The back of the bill will also have a plate serial number and is typically just a one-, two- or three-digit number.

Star numbers

My favorite find is a bill that has a serial number ending in a star instead of a letter. The star notes are used when a bill is removed from a printing run because it was misprinted, damaged or otherwise did not meet quality standards. When the bill is removed, the physical count of bills for that run no longer reconciles with the serial numbers. Re-printing the removed bill is too costly, so it is replaced with a star note. The star notes serial number will be different than its neighbors. I have found star notes in multiple denominations. A sample is shown below. 

Here are some excellent resources for learning more about U.S. currency:

The United States Bureau of Printing and Engraving.

Further information on currency serial numbers.

Evaluate the value of potential rare currency.

Two Ways for Savers to Beat Low Interest Rates

 

Savers are currently earning dismal interest rates on their money accounts and CDs. There are two options to get annual yields of over 3.5% for 20 years and over 9% for at least six months. 

Series EE Savings Bonds offer by Treasury Direct are currently yielding only 0.10%. However, what is not commonly known is that the Treasury promises that your bond will be worth twice what you paid for it if it is held for twenty years.

To estimate what interest rate this doubling over twenty years is equivalent to, one can use the Rule of 72. Divide 72 by 20 yields an approximate interest rate of 3.6%. A great improvement for patient investors willing to hold on to their bonds for twenty years.

The exact interest rate is given by 

2 = (1+i)²⁰

Solving for i, 

i = 2^1/20 – 1 = 0.0353 or 3.53%

In this example, the Rule of 72, provides a good approximation.

The other good offer from the US Treasury is the purchase of I bonds. These bonds have an interest rate that is inflation adjusted every six months. Since the United States has recently experienced a period of higher-than-normal inflation, the interest rate being offered through April 2022 is 7.12%. Next spring, the rate will be adjusted again. I know of no other low-risk investments with 7%+ returns. Investors can buy $10,000 per calendar year. 

Update 5/2/2022 - The treasury announced the I bond rate for the next six months will be 9.62%: Individual - Buying Series I Savings Bonds (treasurydirect.gov)

For information on the rates, Go to: https://www.treasurydirect.gov/indiv/research/indepth/ibonds/res_ibonds.htm#irate

The interest rate was recently adjusted earlier this week and is adjusted, based on inflation, every 6 months (each May and November).

Each person can buy up to $15,000 each year:
Electronic: $10,000, total, each calendar year
Paper: $5,000, total, each calendar year

If you don't have an account already, set one up here: https://www.treasurydirect.gov/RS/UN-AccountCreate.do

Once you have account, you can buy the I-bonds online from Treasury Direct. Next year, you can also buy a paper I bond using your tax refund.

I bonds earn interest for 30 years unless you cash them first. You can cash them after one year. But if you cash them before five years, you lose the previous three months of interest. (For example, if you cash an I bond after 18 months, you get the first 15 months of interest.)

One Hundred Trillion

My last post wrote about the approximate one trillion platelets in my blood donation. Another post described the power of compound interest in which a very modest investment could grow substantially over four hundred years at just a modest interest rate.

There is another example of when interest rates are very high. The enormous multiplying effect doesn't take hundreds of years - only months. That it what led the country of Zimbabwe to issue a one hundred trillion dollar note. At the peak of this period of hyper-inflation around 2007-2009, the cash in your pocket could be worth half, or less, than what it was the day before. In a single year, prior to the issuance of the note shown above, the country issued notes ranging from 10 dollars to 100 billion dollars.

When Zimbabwe gain independence in 1980, their dollar was about worth one United States dollar (USD). When my friend gave me the 100 trillion dollar note shown, it was worth about one USD.

Update 8-17-2021 - see this post for how pi has been calculated to over 62 trillion digits.

How Rare is That Dollar?

The one-dollar bill shown in the photo is somewhat rare. Not so rare that it is worth more than one US dollar, but rare from the perspective of its serial number. That fact may seem surprising. At first glance, the serial number 29573801 doesn't appear extraordinary in any way; it looks just like one of the random 100,000,000 possible serial numbers possible in the 8-digit sequence. You'll see why it is rare after reading the following challenge.

In a prior post, I described a friendly bar bet in which you could easily estimate the number of prime numbers found in a range between two given numbers. A good friend was disappointed with the bar bet because most of his drinking friends don't know what a prime number is. So, I'm offering him a new challenge to try.

Ask your friend to take the first dollar bill out of his wallet or billfold. Without either of you looking at the serial number, he should place it on bar with his hand covering it. Now offer him $10 if the serial number has no repeated digits; if it doesn't, you win the bill. The bill in the photo would be a winner for your friend. Its serial number of 29573801 has no repeated digits. 

The wager is heavily weighted in favor of you. Only about 1 in 55 bills will have a serial number with no repeated digits. 

To see why this occurs so infrequently, consider the specific bill pictured in the photo. Of the digits 0 through 9, it is missing 4 and 6. Let's first calculate the probability that a given bill is missing the digits 4 and 6 and doesn't repeat any of the numbers. Moving through the serial number one place at a time, to meet this criteria, the first digit can be any number except 4 or 6. That leaves 8 digits out of 10. So the probability of getting through the first digit is 8/10. Now, moving to the second digit of the serial number, we need the probability that it is not a 4, 6 or a repeat of the first digit. That leaves 7 digits, so our probability of making it through the first two digits is 8/10 x 7/10. Continuing with all the remaining serial number's digits we find a probability of 8/10 x 7/10 x 6/104 x 5/10 x 4/10 x 3/10 x 2/10 x 1/10 which equals 40320/100,000,000 = .0004032. Next we have to adjust this probability because it was for the very specific case of a bill having no repeated digits and no 4 or 6. There are a total of 45 combinations of the two excluded digits, so our final probability is .000432 x 45 = 0.18144 or roughly 1 in 55.