What values do I enter for N, PMT, i/y, FV and PV on a finance calculator to solve for the question below.

Question

What values do I enter for N, PMT, i/y, FV and PV on a finance calculator to solve for the question below.
If you are willing to pay $47,698.00 today to receive $4,887.00 per year forever then your required rate of return must be ____%. Assume the first payment is received one year from today.

GPT-4o mini · Answer

To solve the problem, we're dealing with a perpetuity. The value of a perpetuity can be calculated using the formula:

$P V = \frac{P M T}{r}$

Where:

$P V$ = Present Value (Amount you pay today)
$P M T$ = Payment received each period (perpetuity payment)
$r$ = Required rate of return (as a decimal)

Given:

$P V = 47, 698$
$P M T = 4, 887$

We want to solve for $r$ : $r = \frac{P M T}{P V}$

Now substituting the given values:

$r = \frac{4, 887}{47, 698}$

Calculating $r$ :

$r = 0.102646 or 10.26$

Now, if you wish to use a finance calculator and input values directly, typically for solving for the rate of return, you'd use the following inputs:

$N$ (Number of periods): Use a very large number (many calculators might allow you to skip this for perpetuity problems)
$P M T$ (Payment): $4, 887$
$i / y$ (Interest rate): Will be solved
$F V$ (Future Value): $0$ (since it’s a perpetuity, we do not consider the future value)
$P V$ (Present Value): $- 47, 698$ (it’s entered as a negative because it’s cash outflow when you pay for the investment)

In summary:

$N$ : can often be left blank for perpetuity or a large number
$P M T$ : 4,887
$i / y$ : Solve for this
$F V$ : 0
$P V$ : -47,698

After inputting these values, use the “compute” feature for $i / y$ to find the required rate of return. It should reflect approximately $10.26$ .