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Chapter 6: Q12Q (page 301)

Question:Assume the same situation as in Question 11, except that the four equal amounts are deposited at the beginning of the period rather than at the end. In this case, what amount must be deposited at the beginning of each period? (Round to two decimals.)

Short Answer

Expert verified

The amount deposited each year is $39177

Step by step solution

01

Step-by-Step SolutionStep 1 Annuity definition

Annuity refers to the financial product which provides specific cash flows at regular intervals of time.

02

Calculation of amount deposited each year

Amountdepositedeachyear=AmountneededRate(futurevalueofanordinaryannuityat10%for4years)=2000004.64100脳1.10=$39177

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Most popular questions from this chapter

Consider the following independent situations. (a) Mike Finley wishes to become a millionaire. His money market fund has a balance of \(92,296 and has a guaranteed interest rate of 10%. How many years must Mike leave that balance in the fund in order to get his desired \)1,000,000? (b) Assume that Sally Williams desires to accumulate \(1 million in 15 years using her money market fund balance of \)182,696. At what interest rate must Sally鈥檚 investment compound annually?

Assume that Wal-Mart Stores, Inc. has decided to surface and maintain for 10 years a vacant lot next to one of its stores to serve as a parking lot for customers. Management is considering the following bids involving two different qualities of surfacing for a parking area of 12,000 square yards.

Bid A: A surface that costs \(5.75 per square yard to install. This surface will have to be replaced at the end of 5 years. The annual maintenance cost on this surface is estimated at 25 cents per square yard for each year except the last year of its service. The replacement surface will be similar to the initial surface.

Bid B: A surface that costs \)10.50 per square yard to install. This surface has a probable useful life of 10 years and will require annual maintenance in each year except the last year, at an estimated cost of 9 cents per square yard.

Instructions Prepare computations showing which bid should be accepted by Wal-Mart. You may assume that the cost of capital is 9%, that the annual maintenance expenditures are incurred at the end of each year, and that prices are not expected to change during the next 10 years.

Using the appropriate interest table, provide the solution to each of the following four questions by computing the unknowns.

(a) What is the amount of the payments that Ned Winslow must make at the end of each of 8 years to accumulate a fund of \(90,000 by the end of the eighth year, if the fund earns 8% interest, compounded annually?

(b) Robert Hitchcock is 40 years old today and he wishes to accumulate \)500,000 by his sixty-fifth birthday so he can retire to his summer place on Lake Hopatcong. He wishes to accumulate this amount by making equal deposits on his fortieth through his sixty-fourth birthday. What annual deposit must Robert make if the fund will earn 8% interest compounded annually?

(c) Diane Ross has \(20,000 to invest today at 9% to pay a debt of \)47,347. How many years will it take her to accumulate enough to liquidate the debt?

(d) Cindy Houston has a \(27,600 debt that she wishes to repay 4 years from today; she has \)19,553 that she intends to invest for the 4 years. What rate of interest will she need to earn annually in order to accumulate enough to pay the debt?

Alan Jackson invests $20,000 at 8% annual interest, leaving the money invested without withdrawing any of the interest for 8 years. At the end of the 8 years, Alan withdraws the accumulated amount of money. Instructions (a) Compute the amount Alan would withdraw assuming the investment earns simple interest. (b) Compute the amount Alan would withdraw assuming the investment earns interest compounded annually. (c) Compute the amount Alan would withdraw assuming the investment earns interest compounded semiannually

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鈥檚 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?
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