Chapter 6

Amortized loans must have which one of these characteristics?

Either equal or unequal principal payments over the life of the loan

You are scheduled to receive annual payments of $3,600 for each of the next 12 years. The discount rate is 8 percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?

$2,170.39 (PMT= 3600, n= 12, I/Y= 8, CPT PV= 27,129.88) (annuity=27,129.88*(1+.08)= 29,300.27) (Diff= 29,300.27-27,129.88= 2,170.39)

You are comparing two annuities with equal present values. The applicable discount rate is 7.25 percent. One annuity pays $2,500 on the first day of each year for 15 years. How much does the second annuity pay each year for 15 years if it pays at the end of each year?

$2,681.25 (PMT= 2500, n=15, I/Y= 7.25, CPT PV= 22,414.55) (annuity= 22,414.55*(1+.0725)= 24,039.61) (PV= 24,039.61, n= 15, I/Y= 7.25, CPT PMT= 2,681.25)

You just purchased an annuity that will pay you $24,000 a year for 25 years, starting today. What was the purchase price if the discount rate is 8.5 percent?

$266,498 (PMT= 24000, n= 25, I/Y= 8.5, CPT PV= 24,562.58) (annuity= 24,562.58 *(1+.085)= 266,498)

Your employer contributes $60 a week to your retirement plan. Assume you work for your employer for another 20 years and the applicable discount rate is 9 percent. Given these assumptions, what is this employee benefit worth to you today?

$28,927.38 (PMT= 60, n= 20*52= 1040, I/Y= 9/52= 0.17, CPT PV= 28,927.38)

You just won the grand prize in a national writing contest! As your prize, you will receive $1,000 a month for 10 years. If you can earn 7 percent on your money, what is this prize worth to you today?

86,126.35 (I/Y=7/12= .58, n= 12*10= 120, PMT= 1000, CPT PV= 86,126.35)

Pure discount

A loan where the borrower receives money today and repays a single lump sum on a future date is called a(n) _____ loan.

Which one of the following statements related to annuities and perpetuities is correct?

A perpetuity composed of $100 monthly payments is worth more than an annuity of $100 monthly payments given equal discount rates

Effective annual rate

An interest rate on a loan that is compounded monthly but expressed as an annual rate would be an example of which one of the following rates?

You are comparing two annuities that offer quarterly payments of $2,500 for five years and pay .75 percent interest per month. You will purchase one of these today with a single lump sum payment. Annuity A will pay you monthly, starting today, while annuity B will pay monthly, starting one month from today. Which one of the following statements is correct concerning these two annuities?

Annuity B has a smaller present value than annuity A

An ordinary annuity is best defined by which one of the following?

Equal payments paid at the end of regular intervals over a stated time period

An amortized loan

May have equal or increasing amounts applied to the principal from each loan payment.

You are comparing two investment options that each pay 6 percent interest, compounded annually. Both options will provide you with $12,000 of income. Option A pays $2,000 the first year followed by two annual payments of $5,000 each. Option B pays three annual payments of $4,000 each. Which one of the following statements is correct given these two investment options? Assume a positive discount rate.

Option B has a higher present value at time zero

Which one of the following statements concerning interest rates is correct?

The effective annual rate equals the annual percentage rate when interest is compounded annually.

Pure discount loan

The entire repayment of which one of the following loans is computed simply by computing one single future value?

Annual percentage rate

The interest rate that is most commonly quoted by a lender is referred to as which one of the following?

Which one of these statements related to growing annuities and perpetuities is correct?

The present value of a growing perpetuity will decrease if the discount rate is increased

How is the principal amount of an interest-only loan repaid?

The principal is repaid in one lump sum at the end of the loan period.

Which one of the following statements correctly defines a time value of money relationship?

Time and present value are inversely related, all else held constant.

Which one of the following accurately defines a perpetuity?

Unending equal payments paid at equal time intervals.

Which one of the following statements related to loan interest rates is correct?

When comparing loans you should compare the effective annual rates

Annual

Which one of the following compounding periods will yield the lowest effective annual rate given a stated future value at year 5 and an annual percentage rate of 10 percent?

Project B is worth less today than Project A

Which one of the following statements is correct given the following two sets of project cash flows? Assume a positive discount rate. Project A Project B Year 1 $4,000 $2,000 Year 2 3,000 3,000 Year 3 0 2,000 Year 4 3,000 3,000

Balloon loan

Which one of the following terms is defined as a loan wherein the regular payments, including both interest and principal amounts, are insufficient to retire the entire loan amount, which then must be repaid in one lump sum?

Interest-only loan

Which one of the following terms is used to describe a loan that calls for periodic interest payments and a lump sum principal payment?

Project X has both a higher present and a higher future value than Project Y (Project X has more money invested)

You are considering two projects with the following cash flows. Which one of the following statements is true concerning these two projects are given a positive discount rate? Project X Project Y Year 1 $8,500 $7,000 Year 2 8,000 7,500 Year 3 7,500 8,000 Year 4 7,000 8,500

As the beneficiary of a life insurance policy, you have two options for receiving the insurance proceeds. You can receive a lump sum of $200,000 today or receive payments of $1,400 a month for 20 years. If you can earn 6 percent on your money, which option should you take and why?

You should accept the $200,000 because the payments are only worth $195,413 to you today (n=12*20= 240, I/Y= 6/12= .5, PMT= 1400, CPT PV = 195,413.08)

Annual percentage rate

Your credit card charges you 1.5 percent interest per month. This rate when multiplied by 12 is called the: