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John Fillmore’s lifelong dream is to own his own fishing boat to use in his retirement. John has recently come into an inheritance of \(400,000. He estimates that the boat he wants will cost \)300,000 when he retires in 5 years. How much of his inheritance must he invest at an annual rate of 8% (compounded annually) to buy the boat at retirement?

Short Answer

Expert verified

The amount of inheritance at an annual rate of 8% will be $204,174.

Step by step solution

01

Definition of inheriting

Inheritance is defined as the passing down of the assets to individuals after the owner of assets dies.

02

Calculation of inheritance

PV=Amount×Rate=300,000×.68058=$204,174

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Most popular questions from this chapter

Ellison Inc., a manufacturer of steel school lockers, plans to purchase a new punch press for use in its manufacturing process. After contacting the appropriate vendors, the purchasing department received differing terms and options from each vendor. The Engineering Department has determined that each vendor’s punch press is substantially identical and each has a useful life of 20 years. In addition, Engineering has estimated that required year-end maintenance costs will be \(1,000 per year for the first 5 years, \)2,000 per year for the next 10 years, and \(3,000 per year for the last 5 years. Following is each vendor’s sales package.

Vendor A: \)55,000 cash at time of delivery and 10 year-end payments of \(18,000 each. Vendor A offers all its customers the right to purchase at the time of sale a separate 20-year maintenance service contract, under which Vendor A will perform all year-end maintenance at a one-time initial cost of \)10,000.

Vendor B: Forty semiannual payments of \(9,500 each, with the first installment due upon delivery. Vendor B will perform all year-end maintenance for the next 20 years at no extra charge.

Vendor C: Full cash price of \)150,000 will be due upon delivery.

Instructions Assuming that both Vendors A and B will be able to perform the required year-end maintenance, Ellison’s cost of funds is 10%, and the machine will be purchased on January 1, from which vendor should the press be purchased?

Andrew Bogut just received a signing bonus of \(1,000,000. His plan is to invest this payment in a fund that will earn 8%, compounded annually. Instructions (a) If Bogut plans to establish the AB Foundation once the fund grows to \)1,999,000, how many years until he can establish the foundation? (b) Instead of investing the entire \(1,000,000, Bogut invests \)300,000 today and plans to make 9 equal annual investments into the fund beginning one year from today. What amount should the payments be if Bogut plans to establish the $1,999,000 foundation at the end of 9 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?

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

For each of the following cases, indicate (a) to what rate columns, and (b) to what number of periods you would refer in looking up the interest factor.

1. In a future value of 1 table Annual Number of Rate Years Invested Compounded

a. 9% 9 Annually b. 12% 5 Quarterly c. 10% 15 Semiannually

2. In a present value of an annuity of 1 table Annual Number of Number of Frequency of Rate Years Involved Rents Involved Rents

a. 9% 25 25 Annually b. 10% 15 30 Semiannually c. 12% 7 28 Quarterly

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