Mr. Dubofsky just won a "Name That Tune" contest with a grand prize of $250,001. However, the contest stipulates that the winner will receive $100,000 immediately, and $15,000 at the end of each of the next 10 years. Assuming that he can earn 5% on his money, how much has he actually won?

Question

Quizplus · Accepted Answer

To calculate the actual amount Mr. Dubofsky has won, we need to consider the present value of the annuity (the $15,000 payments for 10 years) plus the immediate $100,000 payment. The formula for the present value of an annuity is $PV = P \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]$, where $P$ is the payment amount, $r$ is the interest rate per period, and $n$ is the number of periods.Given:- $P = $15,000$- $r = 5\% = 0.05$- $n = 10$The present value of the annuity (the $15,000 payments) is:$$PV = $15,000 \times \left[\frac{1 - (1 + 0.05)^{-10}}{0.05}\right]$$$$PV = $15,000 \times \left[\frac{1 - (1.05)^{-10}}{0.05}\right]$$$$PV = $15,000 \times 7.7217$$ (using a financial calculator or present value table for the factor)$$PV = $115,826.02$$Adding the immediate $100,000 payment:$$Total = $115,826.02 + $100,000 = $215,826.02$$Therefore, the actual amount Mr. Dubofsky has won, considering the present value of future payments at a 5% interest rate, is $215,826.02.

Mr Dubofsky Just Won a "Name That Tune" Contest with a Grand