This problem deals with the concept of a perpetuity, which is a constant stream of cash flows that continue indefinitely. The formula for the present value (PV) of a perpetuity is given by:

$PV = \frac{C}{r}$

Where:

• $PV$ is the present value of the perpetuity,
• $C$ is the annual cash flow (payment),
• $r$ is the interest rate (as a decimal).

We are given:

• $PV = 654,163$ (the cost of the policy),
• $C = 50,000$ (the annual payment),
• $r$ is the unknown interest rate we need to solve for.

Rearranging the formula to solve for $r$:

$r = \frac{C}{PV}$

Substitute the known values:

$r = \frac{50,000}{654,163}$

Let's calculate $r$.The interest rate that would make this a fair deal is approximately 0.0764, or 7.64% when expressed as a percentage.

Would you like further details or have any questions?

Here are five related questions:

1. What is a perpetuity, and how is it different from an annuity?
2. How would the interest rate change if the annual payment was higher or lower?
3. Can a perpetuity formula be used for non-constant payments? Why or why not?
4. What role does inflation play in the value of a perpetuity?
5. How is the concept of present value useful in investment decisions?

Tip: Always be cautious with perpetuities when dealing with real-world investments, as factors like inflation and changing interest rates could affect the future value of money.