Xu owns two investments, A and B, that have a combined total value of $40,000. Investment A is expected to pay $28,000 in 3 years from today and has an expected return of 7.1 percent per year. Investment B is expected to pay $36,000 in T years from today and has an expected return of 5.5 percent per year. What is T, the number of years from today that investment B is expected to pay $36,000?

Answers

Answer 1

Answer:

The number of years is [tex]T =13 \ years[/tex]

Explanation:

From the question we are told that

       The total value of the investment A and B is  [tex]k =[/tex]$40, 000

       The future value of A is [tex]F_A =[/tex]$28,000

       The time period is  t = 3

       The expected return of A is  [tex]e_A =[/tex] 7.1 % =  0.071

       The future value of  B is  [tex]F_B =[/tex]$36,000

        The time period for  B  is T

       The expected return of B is [tex]e_B =[/tex]5.5 % = 0.055

     

The present value of investment A is mathematically represented as

        [tex]A = \frac{F_A }{(1 + e_A) ^t}[/tex]

substituting values

      [tex]A = \frac{ 28000 }{(1 + 0.071) ^3}[/tex]

       [tex]A =[/tex]$ 22792.38

The present value of B is mathematically evaluated as

      [tex]B = k - A[/tex]

  substituting values

     B  =  40, 000 - 22792.38

      B  =  $17,208

The future value of B is

      [tex]F_B = B * (1 + e_B)^T[/tex]

 substituting values

     [tex]36,000 =17,208 * (1 + 0.055)^T[/tex]

     [tex]2.0921 = (1.055)^T[/tex]

take log of both sides

    [tex]log(2.0921) =log (1.055)^T[/tex]

   [tex]0.32057 = T log (1.055)[/tex]

=>   [tex]T = \frac{0.3206}{0.0232}[/tex]

     [tex]T =13 \ years[/tex]

     


Related Questions

A company just starting in business purchased three merchandise inventory items at the following prices. First purchase $60; Second purchase $67; Third purchase $64. If the company sold two units for a total of $209 and used FIFO costing, the gross profit for the period would be

Answers

Answer:

$82

Explanation:

As company Uses FIFO system, it will sell first two products

The cost price =($60 + $67 = 127).

So Gross profit = Selling Price-Cost Price

Gross Profit = 209-127

= $82

The gross profit for the period is $82

Which best describes the role the applicants can fill in the company? Applicants 1 and 3 are best suited to work in network systems, while Applicant 2 could work in programming, information support, or interactive media. Applicants 2 and 3 are best suited to work in network systems, while Applicant 1 could work in programming, information support, or interactive media. Applicant 1 is best suited to work in network systems, while Applicants 2 and 3 could work in programming, information support, or interactive media. Applicant 3 is best suited to work in network systems, while Applicants 2 and 3 could work in programming, information support, or interactive media.

Answers

Incomplete question, however I made interferences from an employer perspective.

Answer:

Applicant 1 is best suited to work in network systems, while Applicants 2 and 3 could work in programming, information support, or interactive media.

Explanation:

From a performance point of view the programming, information support and interactive media roles of the company would be better handled by more than one individual since this roles involve more responsibilities that could not be handled by one individual.

The network systems role can better be managed by Applicant 1 only as it is a task that could be handled by a single employee.

Answer:

C. Applicant 1 is best suited to work in network systems, while Applicants 2 and 3 could work in programming, information support, or interactive media.

Explanation:

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