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:

Problem 5-20 Annuities (LO3) A famous quarterback just signed a $15 million contract providing $3 million a year for 5 years. A less famous recelver 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 b. What is the PV of the receiver's contract? Note: Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places. Present value million

Problem 55−20-20 Annuities (LO33)\newlineA famous quarterback just signed a $15 \$ 15 million contract providing $3 \$ 3 million a year for 55 years. A less famous recelver 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\newlinemillion\newlineb. What is the PV of the receiver's contract?\newlineNote: Do not round intermediate calculations. Enter your answer in millions rounded to 22 decimal places.\newlinePresent value\newlinemillion

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Interpret parts of quadratic expressions: word problemsright chevron icon

Full solution

Q. Problem 55−20-20 Annuities (LO33)\newlineA famous quarterback just signed a $15 \$ 15 million contract providing $3 \$ 3 million a year for 55 years. A less famous recelver 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\newlinemillion\newlineb. What is the PV of the receiver's contract?\newlineNote: Do not round intermediate calculations. Enter your answer in millions rounded to 22 decimal places.\newlinePresent value\newlinemillion
  1. Calculate Present Value: To find the present value of the quarterback's contract, we will use the formula for the present value of an ordinary annuity since the payments are equal and occur at regular intervals. The formula 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. Quarterback's Contract: First, we calculate the present value of the quarterback's contract. The annual payment (PMT) is $3\$3 million, the interest rate (r) is 10%10\% or 0.100.10, and the number of periods (n) is 55 years.\newlinePV=3×(1−(1+0.10)−50.10)PV = 3 \times \left(\frac{1 - (1 + 0.10)^{-5}}{0.10}\right)
  3. Receiver's Contract: Now, we perform the calculations for the exponent and the division:\newlinePV=3×[1−(1.10)−50.10]PV = 3 \times \left[\frac{1 - (1.10)^{-5}}{0.10}\right]\newlinePV=3×[1−0.620920.10]PV = 3 \times \left[\frac{1 - 0.62092}{0.10}\right]\newlinePV=3×[0.379080.10]PV = 3 \times \left[\frac{0.37908}{0.10}\right]\newlinePV=3×3.7908PV = 3 \times 3.7908
  4. Total Present Value: Multiplying the final values gives us the present value of the quarterback's contract:\newlinePV=3×3.7908PV = 3 \times 3.7908\newlinePV=11.3724PV = 11.3724 million
  5. Total Present Value: Multiplying the final values gives us the present value of the quarterback's contract:\newlinePV=3×3.7908PV = 3 \times 3.7908\newlinePV=11.3724PV = 11.3724 millionFor the receiver's contract, we need to calculate the present value of the immediate payment of $4\$4 million and the present value of the annuity of $2\$2 million a year for 55 years.\newlineThe present value of the immediate payment is simply $4\$4 million since it is already in present value terms.
  6. Total Present Value: Multiplying the final values gives us the present value of the quarterback's contract:\newlinePV=3×3.7908PV = 3 \times 3.7908\newlinePV=11.3724PV = 11.3724 millionFor the receiver's contract, we need to calculate the present value of the immediate payment of $4\$4 million and the present value of the annuity of $2\$2 million a year for 55 years.\newlineThe present value of the immediate payment is simply $4\$4 million since it is already in present value terms.Next, we calculate the present value of the annuity part of the receiver's contract using the same formula as before, but with PMT being $2\$2 million.\newlinePVannuity=2×[1−(1+0.10)−50.10]PV_{\text{annuity}} = 2 \times \left[\frac{1 - (1 + 0.10)^{-5}}{0.10}\right]
  7. Total Present Value: Multiplying the final values gives us the present value of the quarterback's contract:\newlinePV=3×3.7908PV = 3 \times 3.7908\newlinePV=11.3724PV = 11.3724 millionFor the receiver's contract, we need to calculate the present value of the immediate payment of $4\$4 million and the present value of the annuity of $2\$2 million a year for 55 years.\newlineThe present value of the immediate payment is simply $4\$4 million since it is already in present value terms.Next, we calculate the present value of the annuity part of the receiver's contract using the same formula as before, but with PMT being $2\$2 million.\newlinePVannuity=2×[1−(1+0.10)−50.10]PV_{\text{annuity}} = 2 \times \left[\frac{1 - (1 + 0.10)^{-5}}{0.10}\right]Performing the calculations for the annuity part:\newlinePVannuity=2×[1−(1.10)−50.10]PV_{\text{annuity}} = 2 \times \left[\frac{1 - (1.10)^{-5}}{0.10}\right]\newlinePVannuity=2×[1−0.620920.10]PV_{\text{annuity}} = 2 \times \left[\frac{1 - 0.62092}{0.10}\right]\newlinePV=11.3724PV = 11.372400\newlinePV=11.3724PV = 11.372411
  8. Total Present Value: Multiplying the final values gives us the present value of the quarterback's contract:\newlinePV=3×3.7908PV = 3 \times 3.7908\newlinePV=11.3724PV = 11.3724 millionFor the receiver's contract, we need to calculate the present value of the immediate payment of $4\$4 million and the present value of the annuity of $2\$2 million a year for 55 years.\newlineThe present value of the immediate payment is simply $4\$4 million since it is already in present value terms.Next, we calculate the present value of the annuity part of the receiver's contract using the same formula as before, but with PMT being $2\$2 million.\newlinePVannuity=2×[1−(1+0.10)−50.10]PV_{\text{annuity}} = 2 \times \left[\frac{1 - (1 + 0.10)^{-5}}{0.10}\right]Performing the calculations for the annuity part:\newlinePVannuity=2×[1−(1.10)−50.10]PV_{\text{annuity}} = 2 \times \left[\frac{1 - (1.10)^{-5}}{0.10}\right]\newlinePVannuity=2×[1−0.620920.10]PV_{\text{annuity}} = 2 \times \left[\frac{1 - 0.62092}{0.10}\right]\newlinePV=11.3724PV = 11.372400\newlinePV=11.3724PV = 11.372411Multiplying the final values gives us the present value of the annuity part of the receiver's contract:\newlinePV=11.3724PV = 11.372411\newlinePV=11.3724PV = 11.372433 million
  9. Total Present Value: Multiplying the final values gives us the present value of the quarterback's contract:\newlinePV=3×3.7908PV = 3 \times 3.7908\newlinePV=11.3724PV = 11.3724 millionFor the receiver's contract, we need to calculate the present value of the immediate payment of $4\$4 million and the present value of the annuity of $2\$2 million a year for 55 years.\newlineThe present value of the immediate payment is simply $4\$4 million since it is already in present value terms.Next, we calculate the present value of the annuity part of the receiver's contract using the same formula as before, but with PMT being $2\$2 million.\newlinePVannuity=2×[1−(1+0.10)−50.10]PV_{\text{annuity}} = 2 \times \left[\frac{1 - (1 + 0.10)^{-5}}{0.10}\right]Performing the calculations for the annuity part:\newlinePVannuity=2×[1−(1.10)−50.10]PV_{\text{annuity}} = 2 \times \left[\frac{1 - (1.10)^{-5}}{0.10}\right]\newlinePVannuity=2×[1−0.620920.10]PV_{\text{annuity}} = 2 \times \left[\frac{1 - 0.62092}{0.10}\right]\newlinePVannuity=2×[0.379080.10]PV_{\text{annuity}} = 2 \times \left[\frac{0.37908}{0.10}\right]\newlinePV=11.3724PV = 11.372400Multiplying the final values gives us the present value of the annuity part of the receiver's contract:\newlinePV=11.3724PV = 11.372400\newlinePV=11.3724PV = 11.372422 millionTo find the total present value of the receiver's contract, we add the present value of the immediate payment to the present value of the annuity:\newlinePV=11.3724PV = 11.372433\newlinePV=11.3724PV = 11.372444 million

More problems from Interpret parts of quadratic expressions: word problems

Question
Solve by completing the square.\newlinem2−10m−29=0m^2 - 10m - 29 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`m` = ____ or `m` = _____
Get tutor helpright-arrow

Posted 2 months ago

Question
Find g(x) g(x) , where g(x) g(x) is the translation 5 5 units up of f(x)=x2 f(x)=x^2 .\newlineWrite your answer in the form a(x–h)2+k a(x–h)^2+k , where a a , h h , and k k are integers.\newlineg(x)= g(x)= ____
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the range of this quadratic function?\newliney=x2−4x+4y = x^2 - 4x + 4\newlineChoices:\newline{y∣y≥2}\left\{y \mid y \geq 2\right\}\newline{y∣y≤0}\left\{y \mid y \leq 0\right\}\newline{y∣y≥0}\left\{y \mid y \geq 0\right\}\newlineall real numbers\text{all real numbers}
Get tutor helpright-arrow

Posted 2 months ago

Question
Write the equation of the parabola that passes through the points (1,0)(1,0), (2,0)(2,0), and (3,–16)(3,\text{–}16). Write your answer in the form y=a(x–p)(x–q)y = a(x – p)(x – q), where aa, pp, and qq are integers, decimals, or simplified fractions.\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinef2+8f+_____f^2 + 8f + \_\_\_\_\_
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve for h h .\newlineh2+39h=0 h^2 + 39h = 0 \newline\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlineh= h = ____\newline
Get tutor helpright-arrow

Posted 2 months ago

Question
Write a quadratic function with zeros −9-9 and −7-7.\newlineWrite your answer using the variable xx and in standard form with a leading coefficient of 11.\newlinef(x)=_____f(x) = \_\_\_\_\_
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the equation of the axis of symmetry for the parabola y=x2y = x^2. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline‾\underline{\hspace{3cm}}
Get tutor helpright-arrow

Posted 3 months ago

Question
Find g(x)g(x), where g(x)g(x) is the translation 88 units up of f(x)=x2f(x) = x^2.\newlineWrite your answer in the form a(x–h)2+ka(x – h)^2 + k, where aa, hh, and kk are integers.\newlineg(x)=g(x) = ______\newline
Get tutor helpright-arrow

Posted 3 months ago

Question
Solve for xx.\newlinex2=1x^2 = 1\newline\newlineWrite your answer in simplified, rationalized form.\newlinex=x = ______ or x=x = ______\newline
Get tutor helpright-arrow

Posted 3 months ago

View all (160)