Final answer:
The present value of Mary Alice's annuity is approximately $3,750,000, using the annuity due present value formula. She would be indifferent between receiving $250,000 per year for 25 years or a lump sum of approximately $3,750,000 today.
Step-by-step explanation:
The subject of this question concerns the concept of present value in Mathematics. Mary Alice is attempting to determine the present value of an annuity, given her option of receiving $250,000 per year for 25 years with the option to earn a 6% investment return. The question asks what lump-sum payment amount would make her indifferent between receiving the annuity and the lump sum.
To find the present value of the annuity, we use the present value formula for an annuity due, since the payments begin today and not at the end of the first period:
PV = Pmt × ((1 - (1 + r)^{-n}) / r) × (1 + r)
Where:
PV = Present Value
Pmt = Annual payment
r = Interest rate per period
n = Number of periods
Plugging in the values:
PV = $250,000 × ((1 - (1 + 0.06)^{-25}) / 0.06) × (1 + 0.06)
PV = $250,000 × ((1 - (1 + 0.06)^{-25}) / 0.06) × 1.06
PV ≈ $3,745,491.03
Therefore, Mary Alice would be indifferent to receiving a lump-sum payment today if it is approximately $3,750,000, which is option (C).