Answer:
To determine at what interest rate the investment policy would be a fair deal, you can use the concept of a perpetuity. In this case, the policy is promising to pay you and your heirs $20,000 per year forever. The value of a perpetuity can be calculated using the following formula:
Perpetuity Value = Payment Amount / Interest Rate
In your case, the payment amount is $20,000 per year. You want to find the interest rate, so rearrange the formula to solve for the interest rate:
Interest Rate = Payment Amount / Perpetuity Value
Now, you are given that the policy costs $465,000, so the perpetuity value is $465,000. Plug in these values to calculate the interest rate:
Interest Rate = $20,000 / $465,000 ≈ 0.043
To express the interest rate as a percentage, multiply by 100:
Interest Rate = 0.043 * 100 ≈ 4.3%
So, for this investment policy to be considered a fair deal, you would need an interest rate of approximately 4.3%. If the actual interest rate you could earn from this investment is greater than 4.3%, it would be a good deal for you. If the actual interest rate is less than 4.3%, it might not be a favorable investment.