The Infinite Treasure: Understanding Present Value of a Perpetuity

In the historic town of Aurelia, an old merchant named Dhruv was known for his wisdom and wealth. One day, as he prepared to retire, he called his two sons, Arjun and Rohan, and presented them with a unique choice:

💰 Option 1: A one-time inheritance of ₹10 crores today.
🏦 Option 2: A mysterious chest that paid ₹10 lakhs every year forever.

Arjun, eager to secure his future, immediately chose the ₹10 crores, thinking it was the wiser option. Rohan, intrigued, asked, “How much is the chest really worth?”

Dhruv smiled and said, “Let’s see if you can figure it out.”

The Wisdom of the Perpetuity

Rohan consulted a mathematician, who explained:
"What you have is called a perpetuity—a financial stream that pays you a fixed amount forever. To find its present value, we use this simple formula:"

$$PV = \frac{C}{r}$$

Where:

• PV = Present Value of the perpetuity
• C = Cash flow per year (₹10 lakhs)
• r = Discount rate (let’s assume 5%)

The Hidden Value

Rohan quickly calculated:

$$\mathrm{<span\; style="font-family:\; Roboto\; Mono;">P</span>}\mathrm{<span\; style="font-family:\; Roboto\; Mono;">V</span>}<span\; style="font-family:\; Roboto\; Mono;">=</span>\frac{\mathrm{<span\; style="font-family:\; Roboto\; Mono;">10</span>}<span\; style="font-family:\; Roboto\; Mono;">,</span>\mathrm{<span\; style="font-family:\; Roboto\; Mono;">00</span>}<span\; style="font-family:\; Roboto\; Mono;">,</span>\mathrm{<span\; style="font-family:\; Roboto\; Mono;">000</span>}}{\mathrm{<span\; style="font-family:\; Roboto\; Mono;">0.05</span>}}<span\; style="font-family:\; Roboto\; Mono;">=</span>\text{<span style="font-family: Roboto Mono;">₹</span>}\mathrm{<span\; style="font-family:\; Roboto\; Mono;">2</span>}\mathrm{<span\; style="font-family:\; Roboto\; Mono;">c</span>}\mathrm{<span\; style="font-family:\; Roboto\; Mono;">r</span>}\mathrm{<span\; style="font-family:\; Roboto\; Mono;">o</span>}\mathrm{<span\; style="font-family:\; Roboto\; Mono;">r</span>}\mathrm{<span\; style="font-family:\; Roboto\; Mono;">e</span>}\mathrm{<span\; style="font-family:\; Roboto\; Mono;">s</span>}$$

He was shocked. The perpetual chest was worth only ₹2 crores in today’s terms—far less than the ₹10 crores Arjun had taken upfront!

The Lesson

Dhruv nodded. “Money loses value over time. Even if something lasts forever, its worth today depends on the returns you could earn elsewhere.”

Arjun smirked. “So, my choice was better?”

Rohan replied, “Only if you invest it wisely. Otherwise, even ₹10 crores will disappear with time.”

And so, both brothers walked away with a lesson: Understanding the time value of money is key to making smart financial decisions.

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Key Takeaways

✅ A perpetuity pays a fixed amount forever.
✅ The present value of a perpetuity is calculated as PV = C / r.
✅ Money now is worth more than money later—so always evaluate options wisely!