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A famous quarterback just signed a $15 million contract providing $3 million a year for 5 years. A less famous receiver signed a $14 million 5 -year contract providing $4 million now and $2 million a year for 5 years. The interest rate is 10%. a. What is the PV of the quarterback's contract? Note: Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places. Present value ◻ million

A famous quarterback just signed a $15 \$ 15 million contract providing $3 \$ 3 million a year for 55 years. A less famous receiver signed a $14 \$ 14 million 55 -year contract providing $4 \$ 4 million now and $2 \$ 2 million a year for 55 years. The interest rate is 10% 10 \% .\newlinea. What is the PV of the quarterback's contract?\newlineNote: Do not round intermediate calculations. Enter your answer in millions rounded to 22 decimal places.\newlinePresent value □\square million

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Q. A famous quarterback just signed a $15 \$ 15 million contract providing $3 \$ 3 million a year for 55 years. A less famous receiver signed a $14 \$ 14 million 55 -year contract providing $4 \$ 4 million now and $2 \$ 2 million a year for 55 years. The interest rate is 10% 10 \% .\newlinea. What is the PV of the quarterback's contract?\newlineNote: Do not round intermediate calculations. Enter your answer in millions rounded to 22 decimal places.\newlinePresent value □\square million
  1. Identify Variables: To find the present value (PV) of the quarterback's contract, we need to discount each of the $3\$3 million payments back to the present value using the formula for the present value of an ordinary annuity. The formula for the present value of an ordinary annuity is PV=PMT×[1−(1+r)−nr]PV = PMT \times \left[\frac{1 - (1 + r)^{-n}}{r}\right], where PMTPMT is the annual payment, rr is the interest rate per period, and nn is the number of periods.
  2. Plug Values into Formula: First, we identify the variables needed for the calculation:\newlinePMTPMT (annual payment) = $3\$3 million\newlinerr (interest rate per period) = 10%10\% or 0.100.10\newlinenn (number of periods) = 55 years
  3. Calculate Present Value: Now we can plug these values into the present value of an ordinary annuity formula:\newlinePV=$3 million×[1−(1+0.10)−50.10]PV = \$3 \text{ million} \times \left[\frac{1 - (1 + 0.10)^{-5}}{0.10}\right]
  4. Round Present Value: Next, we calculate the present value:\newlinePV=($)3 million×[1−(1+0.10)−50.10]PV = (\$)3 \text{ million} \times \left[\frac{1 - (1 + 0.10)^{-5}}{0.10}\right]\newlinePV=($)3 million×[1−(1.10)−50.10]PV = (\$)3 \text{ million} \times \left[\frac{1 - (1.10)^{-5}}{0.10}\right]\newlinePV=($)3 million×[1−0.6209213230591550.10]PV = (\$)3 \text{ million} \times \left[\frac{1 - 0.620921323059155}{0.10}\right]\newlinePV=($)3 million×[0.3790786769408450.10]PV = (\$)3 \text{ million} \times \left[\frac{0.379078676940845}{0.10}\right]\newlinePV=($)3 million×3.79078676940845PV = (\$)3 \text{ million} \times 3.79078676940845\newlinePV=($)11.37236030822535 millionPV = (\$)11.37236030822535 \text{ million}
  5. Round Present Value: Next, we calculate the present value:\newlinePV = $3\$3 million * [1−(1+0.10)−5]/0.10\left[1 - (1 + 0.10)^{-5}\right] / 0.10\newlinePV = $3\$3 million * [1−(1.10)−5]/0.10\left[1 - (1.10)^{-5}\right] / 0.10\newlinePV = $3\$3 million * [1−0.620921323059155]/0.10\left[1 - 0.620921323059155\right] / 0.10\newlinePV = $3\$3 million * [0.379078676940845/0.10]\left[0.379078676940845 / 0.10\right]\newlinePV = $3\$3 million * 33.7907867694084579078676940845\newlinePV = $11.37236030822535\$11.37236030822535 millionFinally, we round the present value to two decimal places as instructed:\newlinePV = [1−(1+0.10)−5]/0.10\left[1 - (1 + 0.10)^{-5}\right] / 0.1000 million

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