The present value of a perpetuity of ₹100 per year, the first payment falling due one year from now, at 5% per annum is:
(a) ₹500
(b) ₹1,000
(c) ₹2,000
(d) ₹5,000

Question

Accepted Answer

For a level perpetuity, $V_{\text{perpetuity}} = \dfrac{P}{i}$ with $P = 100$ and $i = 0.05$:
$$V = \dfrac{100}{0.05} = 2000$$

So the correct option is **(c) ₹2,000**.

**Why the other options are wrong:**
- **(a) ₹500** results from computing $P \times i = 100\times5 = 500$ (or $100/0.20$) — multiplying by the rate instead of dividing.
- **(b) ₹1,000** results from using $i = 10\%$ ($100/0.10$) instead of the given 5%.
- **(d) ₹5,000** results from mistakenly using $i = 2\%$, or from other misplacement of the decimal in the rate.
Only ₹2,000 satisfies the check that a corpus earning 5% yields exactly ₹100 a year: $2000\times0.05 = 100$.

> [!ANSWER]
> **(c) ₹2,000**, since $V = P/i = 100/0.05 = 2000$, and ₹2,000 at 5% earns exactly the ₹100 annual payment forever.

Q.The present value of a perpetuity of ₹100 per year, the first payment falling due one year from now, at 5% per annum is:\n(a) ₹500\n(b) ₹1,000\n(c) ₹2,000\n(d) ₹5,000

Concept understanding — Present Value of an Annuity

Q.The present value of a perpetuity of ₹100 per year, the first payment falling due one year from now, at 5% per annum is:\n(a) ₹500\n(b) ₹1,000\n(c) ₹2,000\n(d) ₹5,000

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