MathMaster logo

MathMaster

  1. Home
  2. general
  3. you have done a great job and your boss offers you a few different possible gifts using a discount rate of 10 which presen
Question

You have done a great job, and your boss offers you a few different possible gifts. Using a discount rate of 10%, which present would you choose? A) A single payment of $75,000 received in 5 years B) $8,000 per year for 10 years, starting two year from now C) One payment of $47,500 received today D) A growing perpetuity that pays $2000 each year starting one year from now. The perpetuity grows at a rate of 1.5% per year. E) All the presents stated are equally good!

230

likes
1152 views

Answer to a math question You have done a great job, and your boss offers you a few different possible gifts. Using a discount rate of 10%, which present would you choose? A) A single payment of $75,000 received in 5 years B) $8,000 per year for 10 years, starting two year from now C) One payment of $47,500 received today D) A growing perpetuity that pays $2000 each year starting one year from now. The perpetuity grows at a rate of 1.5% per year. E) All the presents stated are equally good!

Expert avatar
Nash
4.9
87 Answers
To determine which present is the most valuable, we need to calculate the present value of each option using the given discount rate of 10%.

A) Present value of the single payment of $75,000 received in 5 years:

Using the formula for present value of a single payment:

PV = \frac{FV}{(1 + r)^n}

where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods.

PV = \frac{\$75,000}{(1 + 0.1)^5} = \$54,432.69

B) Present value of $8,000 per year for 10 years, starting two years from now:

Using the formula for present value of an ordinary annuity:

PV = P \times \left(\frac{1 - (1 + r)^{-n}} {r}\right)

where PV is the present value, P is the annuity payment, r is the discount rate, and n is the number of periods.

PV = \$8,000 \times \left(\frac{1 - (1 + 0.1)^{-10}} {0.1}\right) = \$56,877.62

C) Present value of the one payment of $47,500 received today:

The present value is the same as the future value since we are receiving it today.

PV = \$47,500

D) Present value of the growing perpetuity that pays $2000 each year starting one year from now, with a growth rate of 1.5% per year:

Using the formula for present value of a growing perpetuity:

PV = \frac{P}{r - g}

where PV is the present value, P is the payment, r is the discount rate, and g is the growth rate.

PV = \frac{\$2,000}{0.1 - 0.015} = \$23,809.52

Since the present values are different for each option, we can conclude that all the presents stated are not equally good.

Answer: Option B) $8,000 per year for 10 years, starting two years from now, has the highest present value of $56,877.62.

Frequently asked questions (FAQs)
What is the mean, mode, median, range, and average of the following data set: 5, 10, 15, 20, 25, 30?
+
Question: Given an angle of 35 degrees, find the adjacent side using trigonometric rule SOH CAH TOA.
+
Math question: What is the 5th derivative of the function f(x) = 3x^4 - 7x^3 + 2x^2 + 5x - 1?
+
New questions in Mathematics
How to find the value of x and y which satisfy both equations x-2y=24 and 8x-y=117
Pedro bought 9 kg of sugar at the price of R$1.80 per kilogram, six packets of coffee at the price of R$3.90 per packet and 8 kg of rice at the price of R$2.70 per kilogram. Knowing that he paid for the purchases with a R$100.00 bill, how much change did he receive?
What’s the slope of a tangent line at x=1 for f(x)=x2. We can find the slopes of a sequence of secant lines that get closer and closer to the tangent line. What we are working towards is the process of finding a “limit” which is a foundational topic of calculus.
It is known that the content of milk that is actually in a bag distributes normally with an average of 900 grams and variance 25 square grams. Suppose that the cost in pesos of a bag of milk is given by 𝐶(𝑥) = { 3800 𝑠𝑖 𝑥 ≤ 890 4500 𝑠𝑖 𝑥 > 890 Find the expected cost.
P(Z<z)=0.1003
Let v be the set of all ordered pairs of real numbers and consider the scalar addition and multiplication operations defined by: u+v=(x,y)+(s,t)=(x+s+1,y+t -two) au=a.(x,y)=(ax+a-1,ay-2a+2) It is known that this set with the operations defined above is a vector space. A) calculate u+v is au for u=(-2,3),v=(1,-2) and a=2 B) show that (0,0) #0 Suggestion find a vector W such that u+w=u C) who is the vector -u D) show that axiom A4 holds:-u+u=0
Find the minimum value of the function y = -4 x3 + 60 x2 -252 x + 8 for values of x between x = 0 and x = 9 Enter the value of the function, not the value of x
List five numbers that belong to the 5 (mod 6) numbers. Alternate phrasing, list five numbers that satisfy equation x = 5 (mod 6)
Calculate the difference between 407 and 27
A contractor gives a bank note for $10250 at a rate of 1% for one month. How much interest is charged for 4 months?
prove that for sets SS, AA, BB, and CC, where AA, BB, and CC are subsets of SS, the following equality holds: (A−B)−C=(A−C)−(B−C)
At the end of a lively discussion within your study group, your class neighbor, for the relevance of your points of view, asks your opinion on the subject of their debate which is the following question Am I the slave of my unconscious? Solve the problem posed by this subject in an argumentative production.
The blood types of individuals in society are as follows: A: 30%, B: 25%, AB: 20%, 0: 25%. It is known that the rates of contracting a certain disease according to blood groups are as follows: A: 7%, B: 6%, AB: 7%, 0: 4%. Accordingly, if a person selected by chance is known to have this disease, what is the probability of having blood group O?
Cuboid containers (open at the top) should be examined with regard to their volume. The figure below shows a network of such containers (x ∈ Df). Determine a function ƒ (assignment rule and definition area D) that describes the volume of these containers and calculate the volume of such a container if the content of the base area is 16 dm². Show that this function f has neither a local maximum nor a global maximum
To verify that a 1 kg gold bar is actually made of pure gold, a dynamometer is used to record the weight of the bar submerged in water and out of water. a) What would be the value of the weight of the ingot recorded by the dynamometer out of the water? b) What magnitude of thrust does the ingot receive when it is submerged? c) What would the weight of the ingot have to be when it is submerged? Data Pagua = 1000 kg/m³ Pagua= 19300 kg/m³
Identify the slope and y intercept y=11+2/3x
How much does 7.2 moles of ammonium dichromate weigh? (NH4)2Cr2O7
Paul invites 12 friends to his birthday. He wants to give 15 candies to everyone two. The candies are sold in packs of 25. How many should he buy? packages?
Matilde knows that, when driving her car from her office to her apartment, she spends a normal time of x minutes. In the last week, you have noticed that when driving at 50 mph (miles per hour), you arrive home 4 minutes earlier than normal, and when driving at 40 mph, you arrive home 5 minutes earlier later than normal. If the distance between your office and your apartment is y miles, calculate x + y.
A plant found at the bottom of a lake doubles in size every 10 days. Yeah It is known that in 300 days it has covered the entire lake, indicate how many days it will take to cover the entire lake four similar plants.

You might be interested in