Question

Mary Alice just won the lottery and is trying to decide between the options of receiving the annual cash flow payment option of $420,000 per year for 25 years beginning today, or receiving one lump-sum amount today. Mary Alice can earn 6% investing this money. At what lump-sum payment amount would she be indifferent between the two alternatives

Answer 1

Answer:

The lum-sum must equal $5,369,009.59

Explanation:

Giving the following information:

First option:

Annual payment= $420,000

Number of periods= 25 years

Interest rate= 6%

First, we need to calculate the future value of the first option using the following formula:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

FV= {420,000*[(1.06^25) - 1]} / 0.06

FV= $23,043,095.04

Now, to determine the lump-sum to receive today, we need to determine the present worth of the annuity:

PV= FV / (1 + i)^n

PV= 23,043,095.04 / (1.06^25)

PV= $5,369,009.59