A lottery claims its grand prize is $10 million, payable over five years at $2 million...

A lottery claims its grand prize is $10 million, payable over five years at $2 million per year. If the
first payment is made immediately, what is this grand prize really worth? Use an interest rate of 6%.

Solutions

Expert Solution

r = 6%

A_i = lottery amount received in year i

i = year number

Using formula for Present Value

PV_year_i = A_i / (1 + r)ⁱ : ; where i is from 1 to 4

PV_year0 = $2 million

PV_year1 = $2 / (1 + 0.06)¹ = $2 / 1.06 = $1.89 million

PV_year2 = $2 / (1 + 0.06)² = $2 / (1.06)² = $2 / 1.1236 = $1.78 million

PV_year3 = $2 / (1 + 0.06)³ = $2 / (1.06)³ = $2 / 1.1910 = $1.68 million

PV_year4 = $2 / (1 + 0.06)⁴ = $2 / (1.06)⁴ = $2 / 1.2625 = $1.58 million

Present Worth PW = Σ PV_{year i} ; value of i from 0 to 4

= $2 + $1.89 + $1.78 + $1.68 + $1.58

= $8.93 million

The grand prize is really worth $8.93 million

Rahul Sunny answered 1 year ago

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