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FINANCIALLY AESTHETIC · GUIDE 03/37
NET WORTH, INTEREST, INFLATION & TIME VALUE
FA-1.3 · The Money Operating System
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What do you have to start with?
A financial plan is a guide that will help you manage your finances over the long term so you can achieve your life goals. When you’re creating your financial plan, you need to ask yourself: “Where am I today?”, “What are my goals?”, “What do I need to do to achieve them?”
Calculating your net worth is an important step in your financial plan. It will help you answer the question: “What do I have to start with?” Just as with your financial plan, you should update your net worth regularly.
Calculating Net Worth: Assets Minus Liabilities
There are three steps to follow when calculating your net worth.
Step 1: Make a list of all your assets and their values. This includes your savings, investments, real estate, vehicles, and any other assets with monetary value, such as art or collections. Once the list is complete, add up the total value of your assets at current market prices.
Step 2: Make a list of all your debts. For example: credit card balances that you don’t pay off in full at the end of the month, auto loans, student loans, your line of credit balance, mortgage balances, and any other debts, such as taxes payable or money you owe a family member. Once you’ve completed the list, add up the total value of your debts.
Step 3: Calculate your net worth by subtracting your debts from your assets.
Net worth is the total value of your assets minus your debts:
A positive or negative result: what does it mean?
I hope the result is positive! If not, you have a negative net worth, which means your debts exceed your assets. If that’s the case, you should start repaying your debts as soon as possible.
Simple interest and compound interest
Compound interest
Interest calculated on the principal balance, as well as on the accumulated interest.
Simple interest
Interest calculated annually on the initial capital only. Accrued interest during previous periods is not included in calculations for subsequent periods.
Two concepts distinguish how money that is invested - or borrowed - grows over time: simple interest and compound interest.
A savings account earns interest on the money you deposit - the principal. You earn interest on the money in your savings account. Each month, the interest is deposited directly into your account. The higher the interest rate, the more money you make.
With compound interest, your initial deposit earns interest. The money you receive as interest is added to your savings. You’ll continue to earn interest on your total savings. This means you’ll earn interest on your interest. The more frequently your interest is compounded, the faster your balance grows.
Usually, the advertised rate is an annual interest rate. However, interest may be compounded on a monthly or daily basis. Accounts where interest is compounded daily grow faster than those where it is compounded monthly.
An Example of How Compound Interest Is Calculated
Let’s say you deposit $100 into your savings account every month. Your money starts earning interest as soon as you make the deposit. Your account offers an annual interest rate of 2%. Compound interest is calculated on a monthly basis.
This means that each month, you earn approximately 0.167% (2% divided by 12 months) on your balance. This includes the interest paid in previous months.
After one month, you have $100 in your account and earn $0.17 ($100 × 0.167%). After the second month, your interest is calculated on the balance of $200, plus the $0.17 in interest earned in the first month.
On the balance of $200.17, you earn $0.33 in interest ($200 × 0.167%).
Each month, the interest amount you earn increases. At the end of the first year, you earn a total of $13.08 in interest.
The longer you continue to save and earn interest, the more your savings grow.
Why Starting Early Makes All the Difference: The Power of Compound Interest
“Compound interest is the greatest force in the entire universe.” This apocryphal maxim, attributed to Albert Einstein, highlights the power of accumulated interest.
For a saver who lets their investments grow without withdrawing the income, doubling their principal is a matter of return on investment and… time.
An investment yields a 10% return per year. Invest 100 euros, and after one year you have 110 euros. Your initial investment has therefore increased by 10 euros. In the second year, it grows another 10%, which now amounts to 11 euros. So the profit has gone from 10 euros to 11 euros.
The graph described in the source shows what so-called “exponential” growth looks like over 30 years at different rates of return - ranging from 1% per year to 10% per year - for a 1 euro investment.
A steady return of 5% per year means that, for every 1 € invested, you’ll have 2 € after 14 years, 2.65 € after 20 years, and 4.33 € after 30 years.
A steady return of 10% per year means that for every €1 invested, you’ll have €2.59 in 10 years, €6.72 in 20 years, and €17.45 after 30 years!
Exponential growth is simply another way of describing the power of compound interest - that is, interest reinvested with the initial principal.
The Rule of 70
Fortunately, Albert Einstein comes to our rescue with his “Rule of 72,” which provides a quick method for calculating how long it takes for capital to double - a rule that another Albert, Dr. Albert Bartlett, a physics professor at the University of Colorado, rounded to 70 to simplify the calculation even further.
Let’s take, just as an example, the growth of one euro invested:
- €1 invested at 2% - divide 70 by 2. Your capital doubles in 35 years.
- €1 invested at 5% - divide 70 by 5. Your capital doubles in 14 years.
The table below summarizes the time required for the principal to double at different annual rates of return:
| ANNUAL RETURN | ROUNDED TIME (Rule of 70) |
| 1% | 70 years |
| 2% | 35 years |
| 3% | 23.3 years |
| 4% | 17.5 years |
| 5% | 14 years |
| 6% | 12 years |
| 7% | 10 years |
| 8% | 9 years |
| 9% | 8 years |
| 10% | 7 years |
You can also see that a small difference in the annual investment rate leads to significant differences in long-term returns, especially when rates are high.
But your capital doesn’t necessarily double! If you entered the market at the end of 2000 on the CAC 40 (with dividends not reinvested), an investor in French stocks who invested 1 euro would have only 94 centimes left after 20 years - a 6% loss of capital - as of December 31, 2020.
These calculations do not take into account inflation or the cost of taxes, which often varies depending on the taxpayer and the savings plans offered.
Inflation: A General Rise in Prices
Inflation is a situation characterized by a widespread and sustained rise in the prices of goods and services. This situation corresponds to a decline in the purchasing power of money. In short, with the same amount of money, one can buy fewer things than before.
The price level is the average of the prices of all goods and services in the economy at a specific point in time. Inflation measures the rate of change in the price level over a given period.
In France, inflation is measured monthly by INSEE using the Consumer Price Index (CPI). In Canada, it is measured by the Consumer Price Index (CPI). The CPI tracks changes in the prices of more than 600 consumer goods and services over time.
The Bank of Canada aims to keep inflation at 2 percent, which is the midpoint of a target range of 1 to 3 percent. An inflation rate of around 2 percent per year is considered by the European Central Bank (ECB) to be an optimal target.
The Effect of Inflation on Purchasing Power
You can look at the effects of inflation in two ways:
- It raises the cost of the goods and services you buy
- it reduces the purchasing power of your savings over time
For example, a purchase worth $100 made in 2013 would cost about $129 in 2023.
Suppose you plan to retire in 20 years. You want to save enough to buy what $50,000 can buy today. Suppose the inflation rate is 2.5% per year. You will need $81,930 in 20 years.
This also encourages households to invest their excess cash rather than hoard it or keep it in their bank accounts. Otherwise, inflation would erode the purchasing power of their savings.
This penalizes households if their salaries are not indexed to rising prices. They then suffer a loss of purchasing power, which may lead them to reduce their consumption or dip into their savings to maintain their standard of living.
Nominal Value and Real Value
Low inflation also helps keep interest rates at low levels, since the central bank - which sets key interest rates - does not need to tighten credit conditions to achieve its monetary policy objective. This is conducive to economic growth because households and businesses can borrow on favorable financial terms, both in nominal terms (the level of interest rates) and in real terms (the level of interest rates minus inflation).
Once again, inflation erodes the real value of economic agents’ debt. However, it simultaneously erodes the value of their assets.
What Inflation Means for Pensions and Long-Term Savings
You may receive money from public pension plans when you retire. The Old Age Security pension (OAS) and the Canada Pension Plan (CPP) are protected against inflation. This means that as the cost of living rises, the value of your benefits also increases.
Not all employer-sponsored pension plans are protected against inflation. Contact your pension plan administrator or your employer to learn more about your pension.
The Time Value of Money
The Banque de France explicitly uses the concept of the “time value of money” when evaluating future cash flows and then describes a “mechanism for discounting anticipated future cash flows.”
For a beginner, the key concept to remember is simple: two identical amounts available on two different dates are not necessarily equivalent. An amount available today can generate a return; discounting is used to convert a future amount into a comparable value today. It is this logic that links time, interest rates, and the time value of money.
Limitations and Assumptions of Numerical Calculations
The numerical examples provided are based on assumptions that should be kept in mind.
The figures used in the compound interest calculation examples are approximate. Actual results depend on how the financial institution calculates interest. For example, the formula may depend on the number of days in the month. This means that slightly more interest is paid during longer months.
Similarly, calculations of capital doubling using the Rule of 70 do not account for inflation or the cost of taxes, which often varies depending on the taxpayer and the savings plans offered. And as the example of the CAC 40 shows, an average annual return assumes that capital grows continuously: in reality, stock prices can rise or fall each year, and the entry point into a market significantly affects the final result.
Remember that a financial plan is a document that evolves with you and that you should review regularly. Changes in your life or in your financial resources will likely impact your goals and your financial plan. Just as with your financial plan, you should adjust your net worth regularly.
- Investor.gov - Compound Interest Calculator - United States - compounding illustration.
- Financial Consumer Agency of Canada - Start saving for retirement - Canada - inflation and long-term saving.
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