Suppose that you are offered a job for three years, with the following three possible payment options, from which you can choose (all other conditions are equal): Option 1: You are offered $500 for the first month, and each month after you’ll receive an additional amount that increases $50 a month. That is, you’ll receive $500 + $50 = $550 for the second month, and $550 + 100 = $650 for the third month, and $650 + $150 = $800 for the fourth month, etc. Option 2: You are offered $1000 for the first month, and $100 additional dollars each month after. That is, you’ll receive $1100 for the second month, $1200 for the third month, etc. Option 3: You are offered one cent for the first month, and your payment will be doubled each month. That is, you’ll receive 2 cents for the second month, 4 cents for third month, 8 cents for the fourth month, and 16 cents for the fifth month, etc. Construct a table for monthly payments for three years for each of the three options. Make a scatterplot for each option. What type of relation between the time (in months) and payment (in dollars) do you observe in each scatterplot? What properties of the functions did you use to draw your conclusion? Find the equation of the function to calculate the monthly payment in time t (in months) for each of the three options. Use the example for Option 1 as guidance.

EBK CONTEMPORARY FINANCIAL MANAGEMENT

14th Edition

ISBN:9781337514835

Author:MOYER

Publisher:MOYER

Chapter5: The Time Value Of Money

Section: Chapter Questions

Problem 22P

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Suppose that you are offered a job for three years, with the following three possible payment options, from which you can choose (all other conditions are equal):

Option 1: You are offered $500 for the first month, and each month after you’ll receive an additional amount that increases $50 a month. That is, you’ll receive $500 + $50 = $550 for the second month, and $550 + 100 = $650 for the third month, and $650 + $150 = $800 for the fourth month, etc.

Option 2: You are offered $1000 for the first month, and $100 additional dollars each month after. That is, you’ll receive $1100 for the second month, $1200 for the third month, etc.

Option 3: You are offered one cent for the first month, and your payment will be doubled each month. That is, you’ll receive 2 cents for the second month, 4 cents for third month, 8 cents for the fourth month, and 16 cents for the fifth month, etc.

Construct a table for monthly payments for three years for each of the three options.

Make a scatterplot for each option. What type of relation between the time (in months) and payment (in dollars) do you observe in each scatterplot? What properties of the functions did you use to draw your conclusion?

Find the equation of the function to calculate the monthly payment in time t (in months) for each of the three options. Use the example for Option 1 as guidance.

Graph each function and compare it with the scatterplots from (c). Verify that data from the table in (b) matches functions you found in (d).

Use graph all three models in the same coordinate system.

Using graphs or equations of the functions for all three options, answer the following questions:

Will Option 1 ever earn more than Option 2? If so, after how many months will Option 1 be a better choice?
Will Option 3 ever be better than the first two options? If so, after how many months will it be better?

Compare the total payment over six months, one year, eighteen months, two years, and three years for each of the three options. What do you notice? Which option gives you the most money?

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