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Chapter 6: Q13Q (page 301)

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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Answer

The future value of an ordinary annuity is converted to the future value of an annuity due by multiplying with the corresponding value by one plus the interest rate (in decimal figures).

Step by step solution

01

Definition of annuity due

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 calculating the in future ordinary annuity interest involves multiplying the corresponding future values of the ordinary annuity by one plus the interest rate.

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Most popular questions from this chapter

Recently, Glenda Estes was interested in purchasing a Honda Acura. The salesperson indicated that the price of the car was either \(27,600 cash or \)6,900 at the end of each of 5 years. Compute the effective-interest rate to the nearest percent that Glenda would pay if she chooses to make the five annual payments.

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

Sosa Excavating Inc. is purchasing a bulldozer. The equipment has a price of \(100,000. The manufacturer has offered a payment plan that would allow Sosa to make 10 equal annual payments of \)16,274.53, with the first payment due one year after the purchase. Instructions (a) How much total interest will Sosa pay on this payment plan? (b) Sosa could borrow $100,000 from its bank to finance the purchase at an annual rate of 9%. Should Sosa borrow from the bank or use the manufacturer’s payment plan to pay for the equipment?

Danny’s Lawn Equipment sells high-quality lawn mowers and offers a 3-year warranty on all new lawn mowers sold. In 2017, Danny sold \(300,000 of new specialty mowers for golf greens for which Danny’s service department does not have the equipment to do the service. Danny has entered into an agreement with Mower Mavens to provide all warranty service on the special mowers sold in 2017. Danny wishes to measure the fair value of the agreement to determine the warranty liability for sales made in 2017. The controller for Danny’s Lawn Equipment estimates the following expected warranty cash outflows associated with the mowers sold in 2017.

Cash Flow Probability Year Estimate Assessment 2018 \)2,500 20% 4,000 60% 5,000 20% 2019 \(3,000 30% 5,000 50% 6,000 20% 2020 \)4,000 30% 6,000 40% 7,000 30%

Instructions Using expected cash flow and present value techniques determine the value of the warranty liability for the 2017 sales. Use an annual discount rate of 5%. Assume all cash flows occur at the end of the year.

Chris Spear invested $15,000 today in a fund that earns 8% compounded annually. To what amount will the investment grow in 3 years? To what amount would the investment grow in 3 years if the fund earns 8% annual interest compounded semiannually?
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