Future and present value of single sum

The Future Value (FV) and Present Value (PV) of a single sum of money are fundamental concepts in the Time Value of Money (TVM) theory. These concepts help in determining how the value of money changes over time due to interest rates.

Let's break down both of these concepts:

Future Value (FV) of a Single Sum

✅ Definition:

The Future Value (FV) is the value of a single sum of money at a specific point in the future, given a certain interest rate over time.

🧮 Formula:

FV = PV × (1 + r)^n

Where:

• PV = Present Value (the initial amount of money)
• r = Interest rate per period (expressed as a decimal)
• n = Number of periods (years, months, etc.)

🔍 How it Works:

The Future Value is determined by applying the interest rate to the initial investment (PV) over a specified period of time. The formula assumes that the interest is compounded once per period.

📋 Example:

Let’s say you have ₹10,000 today (PV), and you want to find the future value after 3 years at an annual interest rate of 5%.

FV = 10,000 × (1 + 0.05)^3
   = 10,000 × (1.157625)
   = ₹11,576.25

So, the Future Value of ₹10,000 after 3 years at 5% interest would be ₹11,576.25.

Present Value (PV) of a Single Sum

✅ Definition:

The Present Value (PV) is the current value of a future sum of money, discounted by a specific interest rate over a period of time. It’s the reverse calculation of Future Value.

🧮 Formula:

PV = FV / (1 + r)^n

Where:

• FV = Future Value (the amount of money you expect in the future)
• r = Interest rate per period (expressed as a decimal)
• n = Number of periods (years, months, etc.)

🔍 How it Works:

The Present Value is calculated by discounting the future value to the present using the interest rate. This helps in determining how much money needs to be invested today to achieve a specific future amount.

📋 Example:

Let’s say you want to know the present value of ₹15,000 you expect to receive 5 years from now, given an interest rate of 6% annually.

PV = 15,000 / (1 + 0.06)^5
   = 15,000 / (1.338225)
   = ₹11,207.81

So, the Present Value of ₹15,000 that you expect to receive in 5 years at an interest rate of 6% is ₹11,207.81 today.

📊 Comparison: Future and Present Value

🧠 Key Takeaways:

• Future Value (FV): Tells you what an amount of money today will be worth in the future, given a certain interest rate.
• Present Value (PV): Tells you how much money you need to invest today to reach a desired amount in the future.

📚 Why These Concepts Matter:

• Future Value helps in understanding how investments will grow over time (e.g., in retirement planning, saving for a future goal).
• Present Value helps in determining the current worth of future payments or investments (e.g., when deciding whether an investment is worth making today based on future returns).