The present value of a perpetuity of ₹ R payable at the end of each period, when the money is worth i per period is :
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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, R represents the fixed payment received at the end of each period, and i 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 R is discounted by (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+... simplifies to R/i.