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Question:Explain how the future value of an ordinary annuity interest table is converted to the future value of an annuity due interest table.

Short Answer

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The future value of an ordinary annuity is converted to the future value of an annuity due by multiplying with corresponding value by one plus the interest rate

Step by step solution

01

Step-by-Step solutionsStep 1 Annuity due definition

Annuity due refers to an annuity, the payment for which is due just after the starting of each period. Periods can be yearly, half-yearly, and quarterly

02

Conversion to annuity due

The future value of an annuity due can be converted from the future value of an ordinary annuity. The process of in future ordinary annuity interest table is to multiply the corresponding future values of the ordinary annuity by one plus the interest rate.

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Most popular questions from this chapter

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 Jeanโ€™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?

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?

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(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?

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During the past year, Stacy McGill planted a new vineyard on 150 acres of land that she leases for \(30,000 a year. She has asked you, as her accountant, to assist her in determining the value of her vineyard operation.

The vineyard will bear no grapes for the first 5 years (1โ€“5). In the next 5 years (6โ€“10), Stacy estimates that the vines will bear grapes that can be sold for \)60,000 each year. For the next 20 years (11โ€“30), she expects the harvest will provide annual revenues of \(110,000. But during the last 10 years (31โ€“40) of the vineyardโ€™s life, she estimates that revenues will decline to \)80,000 per year.

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