Question

You have been hired as a benefit consultant by Jean Honore, the owner of Attic Angels. She wants to establish a retirement plan for herself and her three employees. Jean has provided the following information. The retirement plan is to be based upon annual salary for the last year before retirement and is to provide 50% of Jean’s last-year annual salary and 40% of the last-year annual salary for each employee. The plan will make annual payments at the beginning of each year for 20 years from the date of retirement. Jean wishes to fund the plan by making 15 annual deposits beginning January 1, 2017. Invested funds will earn 12% compounded annually. Information about plan participants as of January 1, 2017, is as follows.

Jean Honore, owner: Current annual salary of \(48,000; estimated retirement date January 1, 2042.

Colin Davis, flower arranger: Current annual salary of \)36,000; estimated retirement date January 1, 2047.

Anita Baker, sales clerk: Current annual salary of \(18,000; estimated retirement date January 1, 2037.

Gavin Bryars, part-time bookkeeper: Current annual salary of \)15,000; estimated retirement date January 1, 2032.

In the past, Jean has given herself and each employee a year-end salary increase of 4%. Jean plans to continue this policy in the future.

Instructions

(a) Based upon the above information, what will be the annual retirement benefit for each plan participant? (Round to the nearest dollar.) (Hint: Jean will receive raises for 24 years.)

(b) What amount must be on deposit at the end of 15 years to ensure that all benefits will be paid? (Round to the nearest dollar.)

(c) What is the amount of each annual deposit Jean must make to the retirement plan?

Short answer

The annual benefit of Jean is $61,519, Colin is $44,909, Anita is $15,169, and Gravin is $10,390. The required fund balance is $393,270,and the deposit is $9,419.

Step-by-step solution

Part a

$$\begin{gathered} \mathbf{Annual}\mathbf{}\mathbf{retirement}\mathbf{}\mathbf{benefit}\mathbf{}\mathbf{Jean}\mathbf{=}\mathbf{AnnualSalary}\mathbf{\times }\mathbf{FV}\mathbf{}\mathbf{Factor} \\ \mathbf{=}\mathbf{48}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{2}\mathbf{.}\mathbf{56330}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{50} \\ \mathbf{=}\mathbf{\$}\mathbf{61}\mathbf{,}\mathbf{519} \end{gathered}$$

$$\begin{gathered} \mathbf{Annual}\mathbf{}\mathbf{retirement}\mathbf{}\mathbf{benefit}\mathbf{}\mathbf{Colin}\mathbf{=}\mathbf{AnnualSalary}\mathbf{\times }\mathbf{FV}\mathbf{}\mathbf{Factor} \\ \mathbf{=}\mathbf{36}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{3}\mathbf{.}\mathbf{11865}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{40} \\ \mathbf{=}\mathbf{\$}\mathbf{44}\mathbf{,}\mathbf{909} \end{gathered}$$

$$\begin{gathered} \mathbf{Annual}\mathbf{}\mathbf{retirement}\mathbf{}\mathbf{benefit}\mathbf{}\mathbf{}\mathbf{}\mathbf{Anita}\mathbf{=}\mathbf{AnnualSalary}\mathbf{\times }\mathbf{FV}\mathbf{}\mathbf{Factor} \\ \mathbf{=}\mathbf{18}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{2}\mathbf{.}\mathbf{10685}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{40} \\ \mathbf{=}\mathbf{\$}\mathbf{15}\mathbf{,}\mathbf{169} \end{gathered}$$

$$\begin{gathered} \mathbf{Annual}\mathbf{}\mathbf{retirement}\mathbf{}\mathbf{benefit}\mathbf{}\mathbf{Gravin}\mathbf{=}\mathbf{AnnualSalary}\mathbf{\times }\mathbf{FV}\mathbf{}\mathbf{Factor} \\ \mathbf{=}\mathbf{15}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{1}\mathbf{.}\mathbf{73168}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{40} \\ \mathbf{=}\mathbf{\$}\mathbf{10}\mathbf{,}\mathbf{390} \end{gathered}$$

Part B

$$\begin{gathered} \mathbf{Required}\mathbf{}\mathbf{fund}\mathbf{}\mathbf{balance}\mathbf{=}\mathbf{Sum}\mathbf{}\mathbf{total}\mathbf{}\mathbf{of}\mathbf{}\mathbf{all}\mathbf{}\mathbf{annuities} \\ \mathbf{=}\mathbf{61}\mathbf{,}\mathbf{519}\mathbf{\times }\mathbf{2}\mathbf{.}\mathbf{6356}\mathbf{+}\mathbf{44}\mathbf{,}\mathbf{909}\mathbf{\times }\mathbf{1}\mathbf{.}\mathbf{52839}\mathbf{+}\mathbf{15}\mathbf{,}\mathbf{169}\mathbf{\times }\mathbf{4}\mathbf{.}\mathbf{74697}\mathbf{+}\mathbf{10}\mathbf{,}\mathbf{390}\mathbf{\times }\mathbf{8}\mathbf{.}\mathbf{36578} \\ \mathbf{=}\mathbf{\$}\mathbf{393}\mathbf{,}\mathbf{270} \end{gathered}$$

Part C

$$\begin{gathered} \mathbf{FV}\mathbf{=}\mathbf{Deposit}\mathbf{\times }\mathbf{FV}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{annuity}\mathbf{}\mathbf{due} \\ \mathbf{393}\mathbf{,}\mathbf{270}\mathbf{=}\mathbf{Deposit}\mathbf{\times }\mathbf{(}\mathbf{37}\mathbf{.}\mathbf{27972}\mathbf{\times }\mathbf{1}\mathbf{.}\mathbf{12}\mathbf{)} \\ \mathbf{Deposit}\mathbf{=}\mathbf{\$}\mathbf{9}\mathbf{,}\mathbf{419} \end{gathered}$$