Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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 1010%\%. \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.\newline Present value = □\square million

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 6right chevron icon
Debit cards and credit cardsright chevron icon

Full solution

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 1010%\%. \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.\newline Present value = □\square million
  1. Identify Variables: To calculate 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: 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 plug these values into the present value formula for an ordinary annuity:\newlinePV=$3 million×[1−(1+0.10)−50.10]PV = \$3 \text{ million} \times \left[\frac{1 - (1 + 0.10)^{-5}}{0.10}\right]
  4. Round to Two Decimals: Next, we calculate the present value:\newlinePV=($)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 to Two Decimals: 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}Finally, we round the present value to two decimal places as instructed:\newlinePV=$11.37 millionPV = \$11.37 \text{ million}

More problems from Debit cards and credit cards

Question
After returning a few items from online shopping, Luca received a credit of 125125 dollars in his bank account. \newlineWhat does the number 125125 mean? \newlineChoose 11 answer:\newline(A) Luca owes 125125 dollars to the bank. \newline(B) Luca received 125125 dollars in his account.
Get tutor helpright-arrow

Posted 8 months ago

Question
After returning a few items from online shopping, Luca received a credit of 125125 dollars in his bank account. \newlineWhat does the number 125125 mean? \newlineChoose 11 answer:\newline(A) Luca owes 125125 dollars to the bank. \newline(B) Luca received 125125 dollars in his account.
Get tutor helpright-arrow

Posted 8 months ago

Question
Kadeesha's monthly bank statement showed the following deposits and withdrawals:\newline$58.65,−$93.26,−$119.35,$50.73,−$75.50 \$ 58.65,-\$ 93.26,-\$ 119.35, \$ 50.73,-\$ 75.50 \newlineIf Kadeesha's balance in the account was $119.17 \$ 119.17 at the beginning of the month, what was the account balance at the end of the month?\newlineAnswer: $ \$ □\square
Get tutor helpright-arrow

Posted 8 months ago

Question
Ruby's monthly bank statement showed the following deposits and withdrawals:\newline−$91.50,$108.98,−$55.89,−$3.83,$81.61 -\$ 91.50, \$ 108.98,-\$ 55.89,-\$ 3.83, \$ 81.61 \newlineIf Ruby's balance in the account was $112.19 \$ 112.19 at the beginning of the month, what was the account balance at the end of the month?\newlineAnswer: $ \$ □\square
Get tutor helpright-arrow

Posted 8 months ago

Question
Sarah's monthly bank statement showed the following deposits and withdrawals:\newline$115.55,$92.45,−$94.64,$69.81,−$70.08 \$ 115.55, \$ 92.45,-\$ 94.64, \$ 69.81,-\$ 70.08 \newlineIf Sarah's balance in the account was $117.62 \$ 117.62 at the beginning of the month, what was the account balance at the end of the month?\newlineAnswer: $ \$ □\square
Get tutor helpright-arrow

Posted 8 months ago

Question
cost of goods sold totals $300,000\$300,000 for a company, with the inventory beginning balance being $50,000\$50,000 an atory ending balance being $150,000\$150,000. The company has no accounts payable.\newlineUsing the direct method, calculate the adjustment for cash payments made for inventory.\newlinea) $400,000\$400,000\newlineb) $350,000\$350,000\newlinec) $100,000\$100,000\newlined) $200,000\$200,000
Get tutor helpright-arrow

Posted 6 months ago

Question
The operating expenses of a company total $100,000 \$ 100,000 , with the acerued expenses payable beginning balance being $200,000 \$ 200,000 and the accrued expenses payable ending balance being $50,000 \$ 50,000 . The company has no prepaid expenses, amortization, or depreciation.\newlineUsing the direct method, caleulate the adjustment for cash payments of operating expenses.\newlinea) $150,000 \$ 150,000 \newlineb.) $250,000 \$ 250,000 \newlinec) $100,000 \$ 100,000 \newlined) $300,000 \$ 300,000
Get tutor helpright-arrow

Posted 8 months ago

Question
Combine like terms.\newline−2−x+6y−y−7+3−3y -2-x+6 y-y-7+3-3 y \newlineAnswer:
Get tutor helpright-arrow

Posted 8 months ago

Question
Click and drag like terms onto each other to simplify fully.\newline−y2+5y2−3y+3+2y3+3y2−5 -y^{2}+5 y^{2}-3 y+3+2 y^{3}+3 y^{2}-5
Get tutor helpright-arrow

Posted 8 months ago

Question
Click and drag like terms onto each other to simplify fully.\newline4y2+5−3y3+3y3+2y2−7y2−3 4 y^{2}+5-3 y^{3}+3 y^{3}+2 y^{2}-7 y^{2}-3
Get tutor helpright-arrow

Posted 9 months ago

View all (48)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant