Your rich godfather has offered you a choice of one of the three following alternatives: $10,000 now; $2,000 a year for eight years; or $24,000 at the end of eight years. Assuming you could earn 11 percent annually, which alternative should you choose? If you could earn 12 percent annually, would you still choose the same alternative?

Select $24,000 to be received in 8 years

To determine the best alternative, we need to calculate the present value of each option and choose the one with the highest value.

1. $10,000 now:
The present value of the $10,000 is simply $10,000 since it is received immediately.

2. $2,000 a year for eight years:
To calculate the present value, we need to find the present value of each individual $2,000 payment and then sum them up. We can use the formula for the present value of an annuity:

PV = P * [(1 - (1 + r)^(-n)) / r]

Where PV is the present value, P is the payment amount, r is the interest rate per compounding period, and n is the number of compounding periods.

In this case, P = $2,000, r = 11% (0.11 in decimal form), and n = 8.

PV = $2,000 * [(1 - (1 + 0.11)^(-8)) / 0.11]
PV ≈ $12,259.06

3. $24,000 at the end of eight years:
To calculate the present value, we can use the simple present value formula:

PV = FV / (1+r)^n

Where PV is the present value, FV is the future value, r is the interest rate per compounding period, and n is the number of compounding periods.

In this case, FV = $24,000, r = 11% (0.11 in decimal form), and n = 8.

PV = $24,000 / (1 + 0.11)^8
PV ≈ $10,021.02

Comparing the present values for each option:
- $10,000 now: $10,000
- $2,000 a year for eight years: $12,259.06
- $24,000 at the end of eight years: $10,021.02

Therefore, if the interest rate is 11%, the best alternative is to choose the option of receiving $2,000 a year for eight years.

Now, let's examine the scenario with a 12% interest rate.

Using the same calculations:
- $10,000 now: $10,000
- $2,000 a year for eight years: $12,259.06
- $24,000 at the end of eight years: $8,323.66

In this case, the best alternative with a 12% interest rate would still be to choose the option of receiving $2,000 a year for eight years.

In both scenarios, choosing the $2,000 a year for eight years option yields the highest present value, making it the most beneficial choice.