You have been hired as a benefit consultant by Jean Honore, the
owner of Splish 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, 2020. Invested funds will earn 10%
compounded annually. Information about plan participants as of
January 1, 2020, is as follows.
Jean Honore, owner: Current annual salary of $51,520; estimated
retirement date January 1, 2045.
Colin Davis, flower arranger: Current annual salary of $37,900;
estimated retirement date January 1, 2050.
Anita Baker, sales clerk: Current annual salary of $19,110;
estimated retirement date January 1, 2040.
Gavin Bryars, part-time bookkeeper: Current annual salary of
$17,690; estimated retirement date January 1, 2035.
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.
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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. 1.25124 and final answer to 0 decimal
places, e.g. 458,581.)
| Annual Retirement Benefit | ||
| Jean Honore |
$ |
|
| Colin Davis |
$ |
|
| Anita Baker |
$ |
|
| Gavin Bryars |
$ |
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What amount must be on deposit at the end of 15 years to ensure
that all benefits will be paid? (Round factor values to
5 decimal places, e.g. 1.25124 and final answer to 0 decimal
places, e.g. 458,581.)
| The amount must be on deposit |
$ |
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What is the amount of each annual deposit Jean must make to the
retirement plan? (Round factor values to 5 decimal
places, e.g. 1.25124 and final answer to 0 decimal places, e.g.
458,581.)
| The amount of each annual deposit |
$ |
| 1) | |||||
| Jean Honore | Colin Davis | Anita Baker | Gavin Bryars | ||
| Current Annual Salary (A) | $ 51,520.00 | $ 37,900.00 | $ 19,110.00 | $ 17,690.00 | |
| future value of 1, (periods, %) | FV(24,4%) | FV(29,4%) | FV(19,4%) | FV(14,4%) | |
| Future value Factor (B) | 2.56330 | 3.11865 | 2.10685 | 1.73168 | |
| Annual salary during last year of work (A) x (B) | $ 132,061.22 | $ 118,196.84 | $ 40,261.90 | $ 30,633.42 | |
| Retirement benefit % | 50% | 40% | 40% | 40% | |
| Annual retirement benefit | $ 66,031 | $ 47,279 | $ 16,105 | $ 12,253 | |
| Annual Retirement Benefit | |||||
| Jean Honore | $ 66,031 | ||||
| Colin Davis | $ 47,279 | ||||
| Anita Baker | $ 16,105 | ||||
| Gavin Bryars | $ 12,253 | ||||
| 2) | |||||
| Fund requirements after 15 years of deposits at 10% | |||||
| Jean will retire 10 years after deposits stop | |||||
| Annual plan benefit | $ 66,031 | ||||
| X [PV of an annuity due for 30 periods – PV of an annuity due for 10 periods (10.36961 – 6.75902] | 3.61059 | ||||
| Fund balance at the end of the 15 years of deposits. | $ 238,409.45 | ||||
| Colin will retire 15 years after deposits stop. | |||||
| Annual plan benefit | $ 47,279 | ||||
| X [PV of an annuity due for 35 periods – PV of an annuity due for 15 periods (10.60857 – 8.36669] | 2.24188 | ||||
| Fund balance at the end of the 15 years of deposits. | $ 105,993.25 | ||||
| Anita will retire 5 years after deposits stop. | |||||
| Annual plan benefit | $ 16,105 | ||||
| X [PV of an annuity due for 25 periods – PV of an annuity due for 5 periods (9.98474 – 4.16987] | 5.81487 | ||||
| Fund balance at the end of the 15 years of deposits. | $ 93,647.09 | ||||
| Gavin will retire the beginning of the year after deposits stop. | |||||
| Annual plan benefit | $ 12,253 | ||||
| X [PV of an annuity due for 20 periods ] | 9.36492 | ||||
| Fund balance at the end of the 15 years of deposits. | $ 114,751.81 | ||||
| Required fund balance at the end of the 15 years of deposits.: | |||||
| Jean Honore | $ 238,409.45 | ||||
| Colin Davis | $ 105,993.25 | ||||
| Anita Baker | $ 93,647.09 | ||||
| Gavin Bryars | $ 114,751.81 | ||||
| The amount must be on deposit | $ 552,802 | ||||
| 3) | |||||
| Required annual beginning-of-the-year deposits at 10% | |||||
|
Deposit X (future value of an annuity due for 15 periods at 10%) = FV |
|||||
| Deposit X (34.94973 X 1.10) = $552,801.60 | |||||
| Amount of each annual deposit = $552,801.60/38.44470 | $ 14,379 | ||||
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