Undying Life Insurance Company offers an investment policy that will pay you and your heirs $50,000 per year forever. Suppose the company told you the policy costs $654,163. At what interest rate would this be a fair deal? (Do not include the percent sign (%). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

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.

Learn how to calculate the interest rate for a perpetuity investment policy that pays $50,000 per year with a cost of $654,163. This solution uses the perpetuity formula to determine a fair interest rate of 7.64%. Suitable for finance and economics students.

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