Time value of money calculations can be solved using a mathematical equation, a financial calculator, or a spreadsheet. which of the following equations can be used to solve for the present value of a perpetuity? pmt x {1 – [1 / (1+r)n1+rn ]} pv x (1+r)n1+rn fv / (1+r)n1+rn pmtr

To answer this question, we can assume some different possibilities for the answer, since it is incomplete (or with not clear options):

a.

b.

c.  

a.

Step-by-step explanation:

The present value of a perpetuity is an amount of money needed to invest today to have a perpetuity, or an annuity paid for life, considering an interest rate of r.

PMT is a finance term for payment and r is the interest rate (roughly, an important quantity that defines how much it can be obtained for an investment).

In general, the present value can be mathematically defined as:

Where n represents the number of periods for the investment.

On the other hand, an annuity, given a present value PV, is defined by:

Solving this equation for PV (present value) to define the present value of an annuity, we have:

But the question is asking for an annuity paid for life (theoretically, for infinite periods of time); then, if we calculate the limit for the previous equation when n tends to infinity, we find that:

The second term of the previous expression tends to 0 (zero) when n tends to infinity, then:

or

This expression represents that, with an interest of r, if we make an investment of PMT today, then we will have an annuity of for life, because in each period PMT would be the same again due to the interest rate (r).