A state lottery commission pays the winner of the Million Dollar lottery 20 installments of $50,000/year....

A state lottery commission pays the winner of the Million Dollar lottery 20 installments of $50,000/year. The commission makes the first payment of $50,000 immediately and the other n = 19 payments at the end of each of the next 19 years. Determine how much money the commission should have in the bank initially to guarantee the payments, assuming that the balance on deposit with the bank earns interest at the rate of 4%/year compounded yearly. Hint: Find the present value of the annuity. (Round your answer to the nearest cent.)

Solutions

Expert Solution

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

P = Annual Payments

r = rate of interest

n = number of periods

Present value = 50,000*[1 - (1+4%)^-20 / 4% ]*(1+4%)

Present value = 50,000*14.13394

= 706,696.97

jeff jeffy answered 2 years ago

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