Written by Money is one of the most valuable resources in the world.
It can be used to buy goods and services, to invest in businesses and projects, and to save for the future.
But money is not just a static asset that sits in your bank account or wallet.
It has a dynamic value that changes over time. This is what we will discuss in this post: the time value of money (TVM).
Table of Contents
Meaning of the Time Value of Money
The time value of money is the concept that money available at the present time is worth more than the same amount of money in the future due to its potential earning capacity.
It tells us that money today is worth more than money in the future because money today can be invested and earn interest.
Simply said, the value of money today will exceed its value at some point in the future.
For example, if you have $100 today and you invest it at a 10% annual interest rate, you will have $110 after one year.
But if you wait for one year and then receive $100, you will not be able to invest it and earn interest. So, $100 today is worth more than $100 in one year.
So, the time value of money basically states that, because the real or economic value of money decreases over time, it is preferable to receive money now rather than wait for some time in the future.
Components of the time value of money
To compare the value of money at different points in time, we need to use some formulas and concepts.
There are 5 components of the time value of money, which are:
Present Value(PV)
Present value is the value of money today.
It is the current worth of a sum of money that is to be received or paid in the future, discounted or compounded at a specific interest rate.
Present value represents the amount of money you need to invest now to get a certain amount of money in the future.
The formula to solve for present value is:
\(PV = \frac{FV}{\left(1 + \frac{r}{m}\right)^{nm}}\)
Future value(FV)
This is the value of money in the future.
It is the value of a present sum of money at a specified date in the future, assuming a certain interest rate.
Future value represents the amount of money you will have in the future after investing or saving a sum of money today.
\(FV = PV \times \left(1 + \frac{r}{m}\right)^{nm}\)
Interest rate(r or i)
The interest rate is the rate at which money grows over time. It is the rate of return or the cost of borrowing money.
The interest rate significantly affects the present and future values of money.
Even small changes in the interest rate can lead to substantial differences in the final amount.
Number of Years(n)
This is the time horizon of the investment or the loan.
It represents the length of time the money is invested or borrowed.
Compounding Frequency(m)
This represents the number of compounding periods per year.
It is the number of times per year that interest is added to the principal amount of money.
The compounding frequency can be yearly, half-yearly, quarterly, monthly, weekly, daily, or continuously.
The compounding frequency determines how fast money grows over time.
The more frequently interest is compounded, the higher the future value or the lower the present value of money.
For example, if you invest $1,000 for one year at a 10% interest rate compounded annually, you will have $1,100 at the end of the year.
However, if the interest is compounded semiannually, you will have $1,102.50 at the end of the year, because the interest earned in the first six months will also earn interest in the second six months.
Similarly, if the interest is compounded quarterly, you will have $1,103.81 at the end of the year, and so on.
The table below shows the future value of $1,000 for one year at a 10% interest rate with different compounding frequencies.
| Compounding Frequency | Future Value |
|---|---|
| Annually | $1,100.00 |
| Semiannually | $1,102.50 |
| Quarterly | $1,103.81 |
| Monthly | $1,104.71 |
| Weekly | $1,105.06 |
| Daily | $1,105.16 |
| Continuously | $1,105.17 |
As you can see, the future value increases as the compounding frequency increases.
Examples
Now that you have understood the concept of the time value of money concept, I think it will be better to take a practical example.
Example 1
Let’s say you have two options. You can either invest $20,000 today in a business that will give you a 15% return every year, or you can wait for three years and get $25,000 from a relative. Which option will you choose?
Solution:
Let’s calculate the future value of both options to determine which one is financially more advantageous.
Option 1 (Investing Today): Present Value (PV): $20,000, Interest Rate (i): 15% or 0.15, Number of Years (t): 3 years, Compounding Periods (n): 1
Using the Future Value of Money formula:
\(FV = PV \times (1 + \frac{i}{n})^{n \times t}\)
Plugging in the values:
\(FV = $20,000 \times (1 + \frac{0.15}{1})^{1 \times 3}\)
\(FV = $20,000 \times (1.15)^3 = $30,417.50\)
Option 2: $25,000 (to be received in three years)
As you can see, the first option is better than the second one, because you will have more money in the future if you invest today.
By investing $20,000 today, you will have $5,417.50 more than if you wait for three years and get $25,000.
Example 2
Let’s say you want to take a course that costs $10,000. You can either pay for it today, or you can pay for it in two years at the same price. Which option should you choose, if you can earn 6% interest on your money?
Solution:
To compare the two options, we need to calculate the real value of the money we will pay or save for each option.
We can use the same formula as before, but this time we will use it to find the present value.
Option 1 (Paying Today): PV = $10,000
Option 2 (Paying in Two Years): FV = $10,000, r = 6% or 0.06, n = 1, t = 2
\(PV = \frac{FV}{(1 + \frac{r}{n})^{n \times t}}\)
\(PV = \frac{$10,000}{(1 + \frac{0.06}{1})^{1 \times 2}}\)
\(PV = \frac{$10,000}{(1.06)^2} = $8,899.96\)
This means that if you pay for the course in two years, you will only need $8,896.23 today. This is because you can invest that money and earn 6% interest every year.
As you can see, the second option is better than the first one, because you will pay less money today if you wait for two years.
This is the time value of money concept in action: money today is worth more than money tomorrow.
