Would you rather have $100 today or $100 a year from now? Most people would choose today. Money you have now is worth more than the same amount in the future. This is the core idea behind the time value of money.

Why? Because money you have today can be invested and earn interest. That $100 could become $105 in a year. So, the $100 today is actually worth $105 in the future. The opportunity to earn that extra $5 is what gives money its time value.

When you invest or lend money, you expect to get more back than you started with. That extra amount is called interest. There are two main ways to calculate it: simple and compound.

The formula for simple interest is:

$I = P \times r \times t$

Where:

• $I$ is the interest earned
• $P$ is the principal amount
• $r$ is the annual interest rate
• $t$ is the time in years

If you invest $1,000 at a 5% simple interest rate for 3 years, you'd earn $1000 \times 0.05 \times 3 = \text{\textdollar}150$ in interest.

Compound interest is more powerful. It's calculated on the principal amount plus any interest that has already been earned. You earn interest on your interest. Think of it like a snowball rolling downhill; it picks up more snow and gets bigger faster as it goes.

This compounding effect can dramatically increase your investment's value over time. It's why starting to save early is so beneficial.

The time value of money lets us compare the value of money across different points in time using two key calculations: future value and present value.

The formula for future value is based on compound interest:

Here:

• $FV$ is the future value
• $PV$ is the present value (the initial amount)
• $r$ is the interest rate per period
• $n$ is the number of periods

If you invest $1,000 today at an annual rate of 7% for 10 years, its future value would be $1000 \times (1 + 0.07)^{10}$, which is approximately $1,967.

For example, if someone promises to give you $10,000 in five years, what is that promise worth right now? To find out, you can rearrange the FV formula:

Assuming an interest rate (also called a discount rate) of 7%, the present value of that $10,000 is $\frac{10000}{(1 + 0.07)^5}$, which is about $7,130. This means you should be indifferent between receiving $7,130 today and $10,000 in five years, because you could invest the $7,130 at 7% and have $10,000 in five years.

When you invest, you're interested in two main things: the return you might get and the risk you're taking. Basic statistics help us quantify these ideas.

While the mean tells you the expected return, it doesn't tell you anything about the investment's volatility. Did it earn a steady 8% every year, or did it have wild swings? That's where variance and standard deviation come in.

Imagine two investments, A and B, both with an average annual return of 10%. Investment A has a standard deviation of 5%, while Investment B has a standard deviation of 20%. This tells you that Investment A's returns are typically much closer to the 10% average than Investment B's returns. Investment B is the riskier bet; it might have years with huge gains, but also years with significant losses.

Understanding these basic concepts is the first step toward making smart financial choices. They are the building blocks for analyzing everything from a simple savings account to a complex stock portfolio.

Ready to test your knowledge? Let's see what you've learned about the fundamentals of financial math.

Mastering these ideas provides a solid foundation for understanding the world of finance.