Time value of money

Habari! Let's Talk About Money and Time!

Imagine your uncle offers you a gift. You have two choices: receive Ksh 10,000 today via M-Pesa, or receive Ksh 10,000 exactly one year from now. Which one do you choose? I bet most of us would shout, "Leo! Today!"

But why? It's the same amount of money, right? Well, your gut feeling is absolutely correct, and today, we're going to learn the powerful financial principle behind it. Welcome to the lesson on the Time Value of Money (TVM). Simply put, TVM is the concept that a shilling you have today is worth more than a shilling you will receive in the future. Tuko pamoja? Let's break down why.

Why a Shilling Today is a Stronger Shilling

There are three main reasons why money in your hand right now is more valuable than the promise of the same amount later.

• The Power to Earn (Opportunity Cost): Money can work for you! If you get Ksh 10,000 today, you can immediately put it into a Sacco, a money market fund, or even start a small side-hustle. By next year, it will have grown. Leaving it for the future means you miss out on a whole year of potential earnings!
• The Rising Cost of Living (Inflation): Think about the price of a chapati or a plate of chapo madondo. Was it the same price two years ago? Probably not! Inflation is the rate at which the general level of prices for goods and services is rising, and subsequently, purchasing power is falling. The Ksh 10,000 you get next year will likely buy you less than it can today.
• The "What If?" Factor (Risk & Uncertainty): The future is never guaranteed. A promise of future payment comes with risk. What if your uncle forgets? What if his circumstances change? Having the money today eliminates that uncertainty.

Image Suggestion: A vibrant, realistic digital painting of a Kenyan market scene. In the foreground, a person is buying sukuma wiki. A small, transparent graphic overlay shows the price "Ksh 20" with a year "2023" next to it, and another overlay next to it shows "Ksh 25" with the year "2024", visually representing inflation.

The Magic of Compounding: Calculating Future Value (FV)

This is where we see how money grows. Future Value (FV) is the value of a current asset at a future date based on an assumed rate of growth. It's like planting a seed and watching it grow into a tree. The "interest on interest" effect is called compounding.

The formula is your best friend here:

FV = PV * (1 + r)^n

Where:

• FV = Future Value (what you'll have later)
• PV = Present Value (what you have now)
• r = Interest Rate per period (the growth rate)
• n = Number of periods (e.g., years)

Scenario: Investing in a Sacco

Let's say you join a Sacco and deposit Ksh 50,000 (PV). The Sacco pays a very good dividend of 10% per year (r). You want to know how much you'll have after 3 years (n) if you don't touch it. Let's calculate!

Step 1: Identify your variables
PV = 50,000
r = 10% or 0.10
n = 3

Step 2: Plug them into the formula
FV = 50,000 * (1 + 0.10)^3

Step 3: Solve the brackets first
FV = 50,000 * (1.10)^3

Step 4: Calculate the exponent
FV = 50,000 * 1.331

Step 5: Final calculation
FV = 66,550
    

After 3 years, your initial Ksh 50,000 will have grown to Ksh 66,550 without you lifting another finger! That's the power of compounding.

Here is a simple way to visualize it:

      NOW (Year 0)        Year 1        Year 2        Year 3
          |--------------|-------------|-------------|
      Ksh 50,000  -->  Ksh 55,000  --> Ksh 60,500 --> Ksh 66,550
         (PV)         (+10% Int)    (+10% Int)    (+10% Int)  (FV)

Looking Backwards: Calculating Present Value (PV)

Now, let's flip the coin. Present Value (PV) tells us what a future sum of money is worth today. This is also called discounting. It helps you make smart decisions about offers that involve future payments.

The formula is just a rearrangement of the FV formula:

PV = FV / (1 + r)^n

Scenario: The Plot in Kitengela

Someone offers to sell you a plot of land. They give you two payment options: Pay Ksh 400,000 today, or pay Ksh 500,000 in 3 years. To decide which is a better deal, you need to find the present value of that Ksh 500,000. Let's assume you could earn 8% per year (r) in a safe investment.

Step 1: Identify your variables
FV = 500,000
r = 8% or 0.08
n = 3

Step 2: Plug them into the formula
PV = 500,000 / (1 + 0.08)^3

Step 3: Solve the brackets first
PV = 500,000 / (1.08)^3

Step 4: Calculate the exponent
PV = 500,000 / 1.2597

Step 5: Final calculation
PV = 396,919.88
    

The present value of Ksh 500,000 in 3 years is approximately Ksh 396,920. This is less than the Ksh 400,000 they are asking for today! So, from a purely financial standpoint, the future payment is the slightly cheaper option. You see how useful this is?

What About Regular Payments? A Quick Look at Annuities

Life isn't always about single payments. What about regular, consistent payments like saving a fixed amount every month, paying rent, or contributing to a chama? This is called an annuity.

A chama is a perfect Kenyan example of an annuity. Imagine 10 friends agree to contribute Ksh 2,000 every month into a joint investment account. Using TVM formulas for annuities, you can calculate the total value of your chama's investment pot at a future date. It helps you set and reach group financial goals!

Image Suggestion: A vibrant and positive illustration of a group of diverse young Kenyans (around 5-6 people) sitting together in a modern, casual setting like a coffee shop. They are smiling, engaged in a discussion, with a notebook and a laptop on the table. The image should convey a sense of community, collaboration, and financial empowerment, representing a modern 'chama' meeting.

So, Why Does This Matter to You?

Mastering the Time Value of Money is like getting a financial superpower. It helps you:

• Make Smart Savings Goals: You can calculate exactly how much you need to save regularly to reach a future goal, like buying the latest smartphone or starting your own business.
• Evaluate Loans: You can understand the true cost of borrowing money from services like M-Shwari or even a bank.
• Make Big Investment Decisions: Should you invest in shares on the Nairobi Securities Exchange (NSE)? Buy a boda-boda for a transport business? TVM is the foundation for making these critical choices.

You are now equipped with one of the most fundamental principles in finance. Remember, every shilling has potential. By understanding its value over time, you are taking the first major step towards building a secure and prosperous future. Well done!