A lottery promises a $250,000 prize.But the prize money is paid out in $50,000 annual installments with the first installment received today.The winner is offered the option of an immediate lump-sum payment.If the interest rate remains at 10 percent for the entire period, what is the smallest amount the winner should accept?

Question

Quizplus · Accepted Answer

The smallest amount the winner should accept is the present value of the annuity. The annuity consists of 5 payments of $50,000, with the first payment received immediately. The present value of an annuity due (since the first payment is received immediately) can be calculated using the formula for the present value of an annuity due. Given the interest rate of 10%, the present value of this annuity is $208,494. This is the smallest lump sum amount that is equivalent to the annuity payments, considering the time value of money.

A Lottery Promises a $250,000 Prize