Question

Present value of an annuity: lorraine jackson won a lottery. she will have a choice of receiving $25,000 at the end of each year for the next 30 years, or a lump sum today. if she can earn a return of 10 percent on any investment she makes, what is the minimum amount she should be willing to accept today as a lump-sum payment? (round to the nearest hundred dollars.)

A) $321,000
B) $348,000
C) $375,000
D) $402,000

Answer 1

To find the minimum lump-sum payment Lorraine should accept today, we need to calculate the present value of the annuity. The present value of an annuity is calculated using the formula: PV = PMT × [(1 - (1 + r)^-n) / r].

Step-by-step explanation:

To find the minimum lump-sum payment Lorraine should accept today, we need to calculate the present value of the annuity. The present value of an annuity is calculated using the formula:

PV = PMT × [(1 - (1 + r)^-n) / r]

Where PV is the present value, PMT is the annual payment, r is the interest rate, and n is the number of years. In this case, PMT is $25,000, r is 10%, and n is 30 years. Plugging these values into the formula:

PV = $25,000 × [(1 - (1 + 0.10)^-30) / 0.10] = $321,000

Therefore, the minimum amount Lorraine should be willing to accept today as a lump-sum payment is $321,000.