CHAPTER 6 ANSWERS AND SOLUTIONS

Quarterly compounding.com/work/question.php?saved=true&subject=34&subcategory=494&complexity=4#_edn1″ title=””>[i]. Your bank account pays an 8 percent nominal rate of interest. The interest is compounded quarterly. Which of the following statements is most correct?a. The periodic rate of interest is 2 percent and the effective rate of interest is 4 percent.b. The periodic rate of interest is 8 percent and the effective rate of interest is greater than 8 percent.c. The periodic rate of interest is 4 percent and the effective rate of interest is 8 percent.d. The periodic rate of interest is 8 percent and the effective rate of interest is 8 percent.e. The periodic rate of interest is 2 percent and the effective rate of interest is greater than 8 percent.Medium:Annuities.com/work/question.php?saved=true&subject=34&subcategory=494&complexity=4#_edn2″ title=””>[ii]. Suppose someone offered you the choice of two equally risky annuities, each paying $10,000 per year for five years. One is an ordinary (or deferred) annuity, the other is an annuity due. Which of the following statements is most correct?a. The present value of the ordinary annuity must exceed the present value of the annuity due, but the future value of an ordinary annuity may be less than the future value of the annuity due.b. The present value of the annuity due exceeds the present value of the ordinary annuity, while the future value of the annuity due is less than the future value of the ordinary annuity.c. The present value of the annuity due exceeds the present value of the ordinary annuity, and the future value of the annuity due also exceeds the future value of the ordinary annuity.d. If interest rates increase, the difference between the present value of the ordinary annuity and the present value of the annuity due remains the same.e. Statements a and d are correct.Time value concepts.com/work/question.php?saved=true&subject=34&subcategory=494&complexity=4#_edn3″ title=””>[iii]. A $10,000 loan is to be amortized over 5 years, with annual end-of-year payments. Given the following facts, which of these statements is most correct?a. The annual payments would be larger if the interest rate were lower.b. If the loan were amortized over 10 years rather than 5 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 5-year amortization plan.c. The last payment would have a higher proportion of interest than the first payment.d. The proportion of interest versus principal repayment would be the same for each of the 5 payments.e. The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were higher.Time value concepts.com/work/question.php?saved=true&subject=34&subcategory=494&complexity=4#_edn4″ title=””>[iv]. Which of the following is most correct?a. The present value of a 5-year annuity due will exceed the present value of a 5-year ordinary annuity. (Assume that both annuities pay $100 per period and there is no chance of default.)b. If a loan has a nominal rate of 10 percent, then the effective rate can never be less than 10 percent.c. If there is annual compounding, then the effective, periodic, and nominal rates of interest are all the same.d. Statements a and c are correct.e. All of the statements above are correct.Time value concepts.com/work/question.php?saved=true&subject=34&subcategory=494&complexity=4#_edn5″ title=””>[v]. Which of the following statements is most correct?a. An investment that compounds interest semiannually, and has a nominal rate of 10 percent, will have an effective rate less than 10 percent.b. The present value of a 3-year $100 annuity due is less than the present value of a 3-year $100 ordinary annuity.c. The proportion of the payment of a fully amortized loan that goes toward interest declines over time.d. Statements a and c are correct.e. None of the statements above is correct.Tough:Time value concepts.com/work/question.php?saved=true&subject=34&subcategory=494&complexity=4#_edn6″ title=””>[vi]. Which of the following statements is most correct?a. The first payment under a 3-year, annual payment, amortized loan for $1,000 will include a smaller percentage (or fraction) of interest if the interest rate is 5 percent than if it is 10 percent.b. If you are lending money, then, based on effective interest rates, you should prefer to lend at a 10 percent nominal, or quoted, rate but with semiannual payments, rather than at a 10.1 percent nominal rate with annual payments. However, as a borrower you should prefer the annual payment loan.c. The value of a perpetuity (say for $100 per year) will approach infinity as the interest rate used to evaluate the perpetuity approaches zero.d. Statements b and c are correct.e. All of the statements above are correct.Multiple Choice: ProblemsEasy:FV of a sum.com/work/question.php?saved=true&subject=34&subcategory=494&complexity=4#_edn7″ title=””>[vii]. You deposited $1,000 in a savings account that pays 8 percent interest, com­pounded quarterly, planning to use it to finish your last year in college. Eighteen months later, you decide to go to the Rocky Mountains to become a ski instructor rather than continue in school, so you close out your account. How much money will you receive?a. $1,171b. $1,126c. $1,082d. $1,163e. $1,008FV of an annuity.com/work/question.php?saved=true&subject=34&subcategory=494&complexity=4#_edn8″ title=””>[viii]. What is the future value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent interest rate?a. $ 670.44b. $ 842.91c. $1,169.56d. $1,522.64e. $1,348.48FV of an annuity.com/work/question.php?saved=true&subject=34&subcategory=494&complexity=4#_edn9″ title=””>[ix]. Today is your 23rd birthday. Your aunt just gave you $1,000. You have used the money to open up a brokerage account. Your plan is to contribute an additional $2,000 to the account each year on your birthday, up through and including your 65th birthday, starting next year. The account has an annual expected return of 12 percent. How much do you expect to have in the account right after you make the final $2,000 contribution on your 65th birthday?a. $2,045,442b. $1,811,996c. $2,292,895d. $1,824,502e. $2,031,435FV of annuity due