At what rate of interest will the present value of a perpetuity of ₹ 600 payable at the end of every 3 months be ₹ 18,000?

A perpetuity is a series of payments that continue indefinitely. In this case, ₹600 is payable at the end of every 3 months.

For a perpetuity, the relationship between present value, payment, and interest rate per period is:

Present Value $= \dfrac{\text{Payment}}{\text{Interest Rate per period}}$

Rearranging:

Interest Rate per period $= \dfrac{\text{Payment}}{\text{Present Value}}$

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Given information:

• Payment every 3 months = ₹600
• Present Value = ₹18,000
• Payment frequency: Quarterly (every 3 months)

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Quarterly Interest Rate $= \dfrac{600}{18,000}$

$= \dfrac{1}{30}$

$= 0.0333...$

$= 3.33\%$

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Since payments occur 4 times per year (quarterly), the annual interest rate is:

Annual Interest Rate $= 3.33\% \times 4$

$= 13.33\%$

Therefore, the rate of interest is $13.33\%$.