The present value of a perpetuity of ₹ R payable at the end of each period, when the money is worth i per period is :

Answer: The present value of a perpetuity of ₹ R payable at the end of each period, when the money is worth ii per period is Ri\frac{R}{i}.

Step-by-step solution

Step 1: Define Perpetuity

A perpetuity is a stream of equal payments that continues indefinitely. The present value (PV) of a perpetuity is the current value of these future payments, discounted at a specific interest rate.

Step 2: Identify Variables

In this problem, RR represents the fixed payment received at the end of each period, and ii represents the interest rate per period at which the money is worth.

Step 3: Apply the Formula

The formula for the present value of a perpetuity is derived by considering the sum of an infinite geometric series of discounted payments. Each payment RR is discounted by (1+i)(1+i) for each period it is received in the future. The sum of R/(1+i)+R/(1+i)2+R/(1+i)3+...R/(1+i) + R/(1+i)^2 + R/(1+i)^3 + ... simplifies to R/iR/i.

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