1. Fundamental financial concepts
I'm Dakota Wixom, and I'll be your instructor for this course. I'm currently a quantitative finance analyst at a Silicon Valley AI startup called Yewno, where I build innovative financial products out of our New York City office.
2. Course objectives
In this course, you'll learn about the fundamental concepts necessary in order make data-driven financial decisions.
We will cover the time value of money, compound interest, discounting and projecting cash flows, economic decision making, mortgage structures, interest vs equity, the cost of capital, and the basics of wealth accumulation and investment planning.
3. Calculating Return on Investment (% Gain)
To kick things off, let's start with a simple formula to calculate the return, or gain on an investment.
4. Example
Imagine you made a 10,000 dollar investment on year 1, and on year 2 your investment is worth 11,000 dollars. Your investment return is easy to calculate: simply subtract your initial 10,000 dollars from your final 11,000 dollars to calculate your gain of 1,000 dollars, then divide that gain by your initial investment to derive your investment rate of return of 10% on your initial investment over the year.
5. Calculating Return on Investment (Dollar Value)
You can also re-arrange the formula to calculate the dollar value of an investment given a rate of return, r.
6. Example
For example, in this case, if you know the annual rate of return on your investment was 10%, you can multiply the value of your investment, 10,000 dollars, by 1 + 10% to get 11,000 dollars, which matches with the numbers given in the previous example.
7. Cumulative growth (or depreciation)
But what if you have an investment which consistently generates a return year after year, growing larger with each passing period?
The value of an investment with constant cumulative growth over time can be calculated based on r, the investment's expected rate of return (or growth rate), and t, the lifespan of the investment, and v, which is the initial value of the investment at time 0.
Using these simple parameters, we can derive a basic formula to calculate the value of your investment with a constant growth rate over time:
Investment Value = your initial investment times 1 + r, to the power of t.
However, growth rates are often unpredictable in finance rather than constant, and can even be negative, leading to depreciation, which simply means a declining value over time.
8. Discount factors
But what if you know the depreciated value of an investment and the depreciation rate, but you want to calculate the initial value of the investment?
Using simple algebra, you can build a formula to derive the discount factor (df), which is the number that when multiplied by the future value, equals the initial value of the investment.
9. Compound interest
Compounding periods can also change the growth rate of an investment. For example, the interest on your credit card bill is compounded monthly. If it was compounded daily, credit cards would be far more dangerous.
The formula to calculate the cumulative return of an investment with compounding periods is a simple extension of the formula from the previous exercise, dividing r by the number of compounding periods, c, and multiplying t by c as well.
10. The power of compounding returns
Albert Einstein is said to have called compound interest "the most powerful force in the universe".
Here's a simple example of the power of compounded interest over time. Here are two investments, one of which is compounded quarterly. Notice the extra 3 dollars and 81 cents?
So what's the big deal, Einstein?
11. Exponential growth
Well, that number adds up over time, and can be quite significant.
For example, consider what happens over the course of 30 years with the exact same investment.
Quarterly compounding in this example will generate an extra 1,908 dollars and 75 cents over 30 years.
That extra 3 dollars and 81 cents is looking rather important now, isn't it?
Compounding investment returns allows for exponential growth over time.
12. Let's practice!
Now let's try some examples.