### Inflation: Why a Sandwich Costs More Than $5 In 2008 you could famously buy a foot-long sub for$5. In 2020, that same sub costs $6.75. As we look at generating enough passive income to cover our future expenses, we must not just think of how many dollars we will have, but how many sandwiches those dollars can buy! The difference between those two prices is the difference between a nominal price and a real price. Similarly, if we hide$100 under the mattress today, a decade from now we will still have $100 nominal dollars, but will have fewer real dollars, because we can buy less sandwiches with the same money. The green line shows the average price of sandwiches rising over time, with the shaded area projecting 30 years into the future based on the same growth rate. The blue line shows how the number of sandwiches we can buy for the same nominal money decreases as a result. While sandwiches are an illustrative example, this effect touches all goods and services and is known as inflation. In the US, Consumer Price Index (CPI) is a measure tracked by the Bureau of Labor Statistics as measure of generally how much more expensive life is getting. This measure of CPI from the Federal Reserve shows the signature characteristic curve of exponential growth. To calculate the price of something after inflation, we must know the starting price, the rate of inflation, and the time period. For example, if we start with a$5.00 footlong and inflate it at 2.53% for 12 years, we get the following: $Starting\ Price * (1 + Inflation\ Rate)^\text{Number of Years} = Final\ Price$ $5.00 * (1.0253)^{12} = 6.75$
So, what is happening in this equation? We start with the initial price of the sandwich. Then we multiply by the inflation rate. Notice that when we say something is inflating by 2.53%, what we really mean is that it will be 102.53% of the original price. 100% from the original price plus a 2.53% increase. Converting the percentages to decimal form: $100\% = 1$ $2.53\% = 0.0253$ $100\%+2.53\%=1+0.0253=1.0253$
The next step is to use an exponent: we raise 1.0253 to the power of 12, the we are growing over. This calculation gives a growth of 2.53% per year, every year, for 12 years. It is exactly equivalent to just multiplying 1.025 by itself 12 times: $1.0253^{12}=1.0253*1.0253*1.0253*1.0253*1.0253*1.0253*1.0253*1.0253*1.0253*1.0253*1.0253*1.0253$ It is not enough to just add 2.53% per year, as each year’s inflation must start with the previous year’s already inflated price. This is a perfect example of .

CPI has historically averaged 2-3% per year and going forward the US Federal Reserve targets a 2% annual inflation rate. The Fed aren’t omniscient, but they do have some very powerful tools to help push towards this rate. I wouldn’t expect anything drastically different, and this ~2% will work to decay our spending power over time.

Since our spending power is constantly decaying, we must not hide our savings under a mattress. Even savings accounts at banks these days offer interest rates that are well under inflation and should only be utilized to keep cash for short term needs. Instead we invest our savings in stocks, bonds, real estate, or other assets that all work to create a return on our money greater than the rate of the rate of inflation to make sure we can continue to buy sandwiches well into the future.

Bonus:
How did I know 2.53% was the right amount of inflation to grow from $5 to$6.75 over 12 years? If we start with the final price, initial price, and time period we can rework the equation to find the inflation rate: $Starting\ Price * (1 + Inflation\ Rate)^\text{Number of Years} = Final\ Price$
First, divide both sides of the equation by the Starting Price:

${Starting\ Price * (1 + Inflation\ Rate)^\text{Number of Years} \over Starting\ Price} = {Final\ Price \over Starting\ Price}$ ${(1 + Inflation\ Rate)^\text{Number of Years}} = {Final\ Price \over Starting\ Price}$
Next, raise both sides to the power of $\text{(1 / Number of Years)}$:

${(1 + Inflation\ Rate)^\text{Number of Years}}^\text{(1 / Number of Years)} = \left( {Final\ Price \over Starting\ Price} \right)^\text{(1 / Number of Years)}$
When raising a power to another power, you multiply the exponents together to get the resulting power. In this case: $\text{Number of Years} * (1 / \text{Number of Years}) = 1$ Which simplifies our equation to: $(1 + Inflation\ Rate) = \left( {Final\ Price \over Starting\ Price} \right)^\text{(1 / Number of Years)}$
Finally, subtract the 1 from both sides: $Inflation\ Rate = \left( {Final\ Price \over Starting\ Price} \right)^\text{(1 / Number of Years)}-1$ Now we can use the equation to calculate the inflation rate of our sandwich over the last 12 years: $Inflation\ Rate = \left( {6.75 \over 5.00} \right)^{ {\left( 1 \over 12 \right)} }-1 = 0.0253 = 2.53\%$
Like the original form of this equation, this one is more generically useful as well. With a starting amount, ending amount, and number of time periods, we can calculate the rate of return for anything we are interested in, for example a stock or equity index fund. $Growth\ Rate = \left( {Final\ Value \over Initial\ Value} \right)^\text{(1 / Number of Periods)}-1$

### Thrifty Thursday - Save Thousands on Your Phone Plan

Recurring expenses are insidious.  Companies love signing you up for subscription services as it means a consistent revenue stream by default.  The burden is on the consumer to take action, but momentum and inaction usually win out and the payments keep getting made. Taking a hard look at these subscriptions and other recurring payments can be very effective in reducing annual expenses, thereby lowering your Target FI Number and leaving more money for saving and investing .   Some expenses that don’t bring enough value can be eliminated.   Others can be greatly reduced with a little intentionality (just get a month or two of that streaming service to binge your favorite show, no need to leave it renewing for the whole year!)   However, there are some that are necessary but we can work on reducing their impact. One of my favorite hacks is switching to a low-cost cell phone plan offered by a Mobile Virtual Network Operator.    MVNOs lease bandwidth on existing cell towers ins

### Intentional Spending

Your spending is an important factor in your financial independence journey. It effects the rate at which you can save and invest while in the accumulation phase and is also a critical factor in calculating your Target FI Number. When accumulating wealth, the amount you can save and invest is a simple calculation: what you make minus what you spend.  Like many of the levers we talk about, your spending has a non-liner effect on your FI journey.  Spending slightly less also means saving slightly more and both of those quantities are found in the formula for Stash Rate , leading to a multiplied effect. $Stash Rate = {Annual\ Savings \over Annual\ Expenses}$ As we saw in the Stash Rate article, decreasing expenses leads to an exponentially increasing rate of wealth building. On the other side of financial independence, the level of spending in your drawdown phase directly determines your Target FI Number.  Target\ FI\ Numbe

### Stocks: How to Pay Someone Else to Work for You

When you work for a company, you work to build someone else’s wealth.  When you own a company, other people work to build your wealth. Fortunately, you don’t have to be Bill Gates or Elon Musk to own a profitable company.   Instead, as we touched on briefly in the article on assets vs. liabilities , you can buy stock in the company.   Buying a share of stock mean you actually own a small piece of a company. One of the most efficient ways to own stocks is by purchasing low-cost index funds.   These funds can either be in the form of mutual funds or Exchange Traded Funds (ETFs).   The key difference to a traditional actively managed fund is that the index fund simply tracks the relevant market.   For example, an S&P 500 index fund would hold shares of the largest 500 U.S. companies In the S&P 500’s case, the largest 500 with some consistent caveats: at least 10% must be publicly available for trade