Compounding Periods

Compounding refers to earning interest on both the money you originally invest and on the interest that money earns over time. 

Time Value of Money Calculations

We can solve for any one of the following four potential unknowns: future value, present value, the discount rate, or the number of periods. The following lists formulas that can be used in Excel to solve for each input in the time value of money equation.

To Find                               Enter This Formula

Future value                  = FV (rate,nper,pmt,pv)
Present value                = PV (rate,nper,pmt,fv)
Discount rate                = RATE (nper,pmt,pv,fv)
Number of periods    = NPER (rate,pmt,pv,fv)

For example:

If we invest $25,000 at 12 percent, how long until we have $50,000?

The Power of Compound Interest

 Benjamin Franklin once said, “Money makes money, and the money that money makes, makes more money.”

It’s not just a clever line — it’s one of the most powerful truths about building wealth. This is the magic of compound interest.

When you invest, your money starts earning interest. Then that interest earns even more interest. Over time, this creates a beautiful chain reaction — your money grows on its own, faster and faster. 

Think of it like planting a seed.  At first, it’s small. But with time, patience, and consistency, it grows into a tree that bears fruit year after year. You don’t need to start with a lot — you just need to start early and stay consistent. The longer your money has to grow, the more powerful compound interest becomes.

Let your money work for you, not the other way around.

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💪