The Foundations of Financial Decisions

When it comes to making smart financial choices — whether you’re investing, saving, or evaluating a project, three key concepts always come into play: 

Future Value (FV), 

Present Value (PV), 

and Net Present Value (NPV)

Let’s break them down in simple terms

🔹 Future Value (FV)

Future Value tells you how much your money today will be worth in the future, assuming it earns interest or grows over time.

Formula:

$$FV=PV\times (1+r{)}^n$$

Where:

• PV = Present Value (today’s money)

• r = interest rate (per period)

• n = number of periods

💡 Example:
If you invest 10,000 $ at an annual rate of 10% for 3 years,

$$FV=10,000\times (1+0.10{)}^3=13,310$$

So, your money grows to 13,310 $ after 3 years.

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🔹 Present Value (PV)

Present Value tells you how much a future amount of money is worth today, considering the time value of money — the idea that a Toman today is worth more than a Toman tomorrow.

Formula:

$$PV=\frac{FV}{(1+r{)}^{\mathrm{n}}}$$

💡 Example:
If you expect to receive 13,310 $ in 3 years and the discount rate is 10%,

$$PV=\frac{13,310}{(1+0.10{)}^3}=10,000$$

So, the future 13,310 Toman is worth 10,000 $ today.

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🔹 Net Present Value (NPV)

Net Present Value is used to evaluate investments or projects. It’s the difference between the present value of cash inflows and the present value of cash outflows.

Formula:

$$NPV=\sum \frac{R_t}{(1+r{)}^t}-I$$

Where:

• Rₜ = cash inflow at time t

• r = discount rate

• I = initial investment

💡 Example:
You invest 40,000 $ today and expect 15,000 $ annually for 3 years at a 10% discount rate:

$$NPV=\frac{15,000}{1.1}+\frac{15,000}{{1.1}^2}+\frac{15,000}{{1.1}^3}-40,000=3,735$$

 Since the NPV is positive (3,735), the investment is considered profitable.

If the NPV is negative, the financial consultant should not make to purchase or invest.

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 Why It Matters

Understanding FV, PV, and NPV helps you:

• Make smarter investment decisions
  
• Compare projects or savings options
  
• Understand the real value of money over time💪