Question

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You have just won the lottery and will receive $650,000 in one year. You will receive payments for 16 years, and the payments will increase 4 percent per year. If the appropriate discount rate is 12 percent, what is the present value of your winnings?

Answer 1

Answer :

We know that,

Present value of growing annuity = [ P / ( r - g ) ] * [ 1 - [( 1 + g ) / ( 1 + r )]^n ]

Where,

Interest per annum = 12%

No. of years = 16

Number of compoundings per annum = 1

Interest rate per period ( r ) = 12% / 1 = 12%

No. of periods ( n ) = 16 * 1 = 16

Growth rate ( g ) = 4.00%

First payment ( P ) = $ 650,000

Now,

Present value of growing annuity = [ 650,000 / ( 12% - 4% ) ] * [ 1 - [( 1 + 4% ) / ( 1 + 12% )]^16 ]

Present value of growing annuity = $ 5,642,619