You have been hired as a benefit consultant by Jean Honore, the owner of Crane 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 $1,2025.$ Invested funds will earn $11\%$ compounded annually. Information about plan participants as of January $1,2025,$ is as follows.

Jean Honore, owner: Current annual salary of $$50,880$; estimated retirement date January $1,2050.$

Colin Davis, flower arranger: Current annual salary of $$38,550$; estimated retirement date January $1,2055.$

Anita Baker, sales clerk: Current annual salary of $$20,970$; estimated retirement date January $1,2045.$

Gavin Bryars, part$-$time bookkeeper: Current annual salary of $$16,720$; estimated retirement date January $1,2040.$

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.

$($a$)$

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Based upon the above information, what will be the annual retirement benefit for each plan participant? $($Hint: Jean will receive raises for $24$ years.$)($Round factor values to $5$ decimal places, e$.$g$.1\mathrm{.}25124$ and final answer to $0$ decimal places, e$.$g$.458,581.$

Annual Retirement Benefit

Jean Honore $$

Colin Davis

$

Anita Baker $$

Gavin Bryars

$ $$How to solve

You have been hired as a benefit consultant by Jean Honore, the owner of Crane 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 $1,2025.$ Invested funds will earn $11\%$ compounded annually. Information about plan participants as of January $1,2025,$ is as follows.

Jean Honore, owner: Current annual salary of $$50,880$; estimated retirement date January $1,2050.$

Colin Davis, flower arranger: Current annual salary of $$38,550$; estimated retirement date January $1,2055.$

Anita Baker, sales clerk: Current annual salary of $$20,970$; estimated retirement date January $1,2045.$

Gavin Bryars, part$-$time bookkeeper: Current annual salary of $$16,72G$; estimated retirement date January $1,2040.$

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.

Based on the info above, the annual retirement benefit for each plan participant is as follows:

Jean Honore$-$ $$65,212$

Colin Davis$-$ $$48,090$

Anita Baket$-$ $$17,672$

Gavin Bryars$-$ $$11,582$

What amount must be on deposit at the end of $15$ years to ensure that all benefits will be paid?

What is the amount of each annual deposit jean must make to the retirement plan?