Chapter 9

Assume your bank has a choice between two deposit accounts. Account A has an annual percentage rate of 4.62 percent with interest compounded monthly. Account B has an annual percentage rate of 4.62 percent but with interest compounded quarterly. Which account provides the highest effective annual return?

Account A

Assume your bank has a choice between two deposit accounts. Account A has an annual percentage rate of 7.55 percent with interest compounded monthly. Account B has an annual percentage rate of 7.45 percent with interest compounded quarterly. Which account provides the higher effective annual return?

Account A

Jonathan borrows $10,500 from the bank at 11 percent annually compounded interest to be repaid in six equal annual installments, with the payments being made at the end of each year. The amount paid toward interest in the first year's payment is: Pick the closest answer.

$1,115

What would be the future value of a CD of $1,000 for two years if the bank offered a 10% interest rate compounded semiannually? Pick the closest answer.

$1,216

Megan puts $1,000 in a savings passbook that pays 4% compounded quarterly. How much will she have in her account after five years? Pick the closest answer.

$1,220.20

If $1,000 were invested now at a 12% interest rate compounded annually, what would be the value of the investment in two years? Pick the closest answer.

$1,254

Jonathan borrows $10,500 from the bank at 11 percent annually compounded interest to be repaid in six equal annual installments, with the payments being made at the end of each year. The amount paid toward the principal in the first year's payment is: Pick the closest answer.

$1,326.91

Olivia borrows $4,500 at 12 percent annually compounded interest to be repaid in four equal annual installments. The actual end-of-year payment is: Pick the closest answer.

$1,482

Assume that a borrower is willing to pay you $2,000 at the end of three years in return for a sum of money now. To receive a return of 10%, what is the most you should be willing to lend now? Pick the closest answer.

$1,503

The present value of an ordinary annuity of $350 each year for five years, assuming an opportunity cost of 4 percent, is: Pick the closest answer.

$1,558.14

A wealthy inventor has decided to endow her favorite art museum by establishing funds for an endowment which would provide $1,000,000 per year forever. She will fund the endowment upon her fiftieth birthday 10 years from today. She plans to accumulate the endowment by making annual end-of-year deposits into an account. The rate of interest is expected to be 5 percent in all future periods. How much must the scientist deposit each year to accumulate to the required amount? Pick the closest answer.

$1,590,091

Assume a lender offers you a $25,000, 10%, three-year loan that is to be fully amortized with three annual payments. The first payment will be due one year from the loan date. How much will you have to pay at the end of each year? Pick the closest answer.

$10,053

Megan is planning for her son's college education to begin five years from today. Megan estimates the yearly tuition to be $5,000 per year for a four-year degree. Tuition must be paid at the beginning of each year. How much must Megan deposit today, at an interest rate of 8 percent, for her son to be able to withdraw $5,000 per year for four years of college? Pick the closest answer.

$12,173

The future value of $100 received today and deposited at 6 percent compounded semiannually for four years is: Pick the closest answer.

$126.67

Lance plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 20 years. If he can earn 12 percent on his contributions, how much will he have at the end of the twentieth year? Pick the closest answer.

$144,105

Gavin makes annual end-of-year payments of $5,043.71 on a four-year loan with an interest rate of 13 percent. The original principal amount was: Pick the closest answer.

$15,002

Gavin wishes to accumulate $1 million by making equal annual end-of-year deposits over the next 20 years. If he can earn 10 percent on his investments, how much must he deposit at the end of each year? Pick the closest answer.

$17,460

A hospital received a contribution to its endowment fund of $2 million. The hospital can never touch the principal, but it can use the earnings. At an assumed interest rate of 9.5 percent, how much can the hospital earn to help its operations each year? Pick the closest answer.

$190,000

$2,000 invested today at 6% in 3 years would result in a future value of: Pick the closest answer.

$2,382

Lance would like to send his parents on a cruise for their 50th wedding anniversary. He expects the cruise will cost $15,000 and he has 5 years to accumulate this money. How much must Lance deposit at the end of each year in an account paying 10 percent interest in order to have enough money to send his parents on the cruise? Pick the closest answer.

$2,457

You put $2,000 in an IRA account at Northern Trust. This account pays a fixed interest rate of 8% compounded quarterly. How much money do you have in five years? Pick the closest answer.

$2,972

Kristen plans to start her college education four years from now. To pay for her college education, she has decided to save $1,000 at the end of each quarter for the next four years in a bank account paying 12 percent interest compounded quarterly. How much will she have at the end of the fourth year? Pick the closest answer.

$20,157

A ski chalet in Vail now costs $250,000. Inflation is expected to cause this price to increase at 5 percent per year over the next 10 years before Larry and his wife retire from successful investment banking careers. How large an equal annual end-of-year deposit must be made into an account paying an annual rate of interest of 13 percent in order to buy the ski chalet upon retirement? Pick the closest answer.

$22,108

The future value of $200 received today and deposited at 8 percent for three years is: Pick the closest answer.

$251.94

The future value of $200 received today and deposited for three years in an account which pays 8 percent interest compounded quarterly is _________. Pick the closest answer.

$253.65

A generous benefactor to the local university plans to make a one-time endowment which would provide the university with $150,000 per year into perpetuity. The rate of interest is expected to be 5 percent for all future time periods. How large must the endowment be? Pick the closest answer.

$3,000,000

The present value of $1,000 received at the end of year 1, $1,200 received at the end of year 2, and $1,300 received at the end of year 3, assuming an opportunity cost of 7 percent, is: Pick the closest answer.

$3,043.90

Collin plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 10 years. If Collin can earn 10 percent on his contributions, how much will he have at the end of the tenth year? Pick the closest answer

$31,875

Shannon plans to fund his individual retirement account (IRA) with the maximum contribution of $2,500 at the end of each year for the next 30 years. If Shannon can earn 10 percent on his contributions, how much will he have at the end of the tenth year? Pick the closest answer.

$39,844

Lance deposits $2,000 per year at the end of the year for the next 15 years into an IRA account that currently pays 7%. How much will Lance have on deposit at the end of the 15 years? Pick the closest

$50,258

The present value of an annuity of $5,000 to be received at the end of every six months for 6 years at a 4% annual rate would be (Pick the closest answer.):

$52,877

Jonathan borrows $10,500 from the bank at 11 percent annually compounded interest to be repaid in six equal annual installments, with the payments being made at the end of each year. The loan balance at the end of the second year is: Pick the closest answer.

$7,700.17

$100 is received at the beginning of year 1, $200 is received at the beginning of year 2, and $300 is received at the beginning of year 3. If each of these cash flows is deposited at 12 percent on the day they are received, their combined future value at the end of year 3 is: Pick the closest answer

$727.37

Taylor deposits $2,000 per year at the end of the year for the next 20 years into an IRA account that pays 6%. How much will Taylor have on deposit at the end of 20 years? Pick the closest answer.

$73,572

The future value of an ordinary annuity of $1,000 each quarter for 10 years, deposited at 12 percent compounded quarterly is: Pick the closest answer.

$75,401

Kristen has just purchased a used Mercedes for $18,995. She plans to make a $2,500 down payment on the car. What is the amount of her monthly payment on the loan if she must pay 12% annual interest on a 24-month car loan? Pick the closest answer.

$776.48

Taylor has just accepted a job as a stockbroker. He estimates his grosseach year for the next three years is $35,000 in year 1, $21,000 in year 2, and $32,000 in year 3. His gross pay is received at the end of each year. Calculate the present value of these cash flows, if they are discounted at 4%. Pick the closest answer

$81,517.10

Select ALL of the following variables you would not enter into your financial calculator to calculate the future value five years from today of $2,500 deposited today.

-future value(FV) - inflation rate (I) - Payments

You want to buy a Volvo in seven years. The car is currently selling for $50,000, and the price will increase at a compound rate of 10% per year. For the next seven years you can make deposits in an account earning 14% per year compounded annually. How much must you deposit at the end of each of the next seven years to be able to pay cash for your dream car in seven years? Pick the closest answer.

$9,080.20

Jonathan borrows $10,500 from the bank at 11 percent annually compounded interest to be repaid in six equal annual installments, with the payments being made at the end of each year. The loan balance at the end of the first year is: Pick the closest answer.

$9,173.09

Select ALL of the following that are variables used in your financial calculator for time value of money calculations for an annuity.

- present value (PV) - future value (FV) - interest rate (I/Y) - Number of periods (N) - Payment (PMT) - begin/end mode (BGN/END)

Select ALL of the following that are variables used in your financial calculator for time value of money calculations for a single lump sum of money

-present value (PV) - future value (FV) - interest rate (I/Y) - number of periods (N)

Taylor owns stock in a company which has consistently paid a growing dividend over the last 10 years. At the end of the first year Taylor owned the stock, he received $4.50 per share and at the end of the 10th year, he received $4.92 per share. What is the growth rate of the dividends during this time? Pick the closest answer.

1%

Claire bought 100 shares of Minnesota Mining and Manufacturing in June, 1987 for $38 a share for a total investment of $3,800. She sold the shares in June, 1996 for $8,960. What is Cecilia's annual rate of return on her investment? Pick the closest

10%

If the quarterly rate of interest is 2.5% and interest is compounded quarterly, then the APR is: Pick the closest answer.

10.00%

If the quarterly rate of interest is 2.5% and interest is compounded quarterly, then the EAR is: Pick the closest answer.

10.38%

If the APR is 12% and interest is compounded monthly, then the EAR is: Pick the closest answer.

12.68%

What is the highest effective annual rate attainable with a 12 percent nominal rate? Pick the closest answer

12.72%

You deposit $1,000 in a long-term certificate of deposit with an interest rate of 8.81%. How many years will it take for you to triple your deposit? Pick the closest answer.

13 years

Shelby was given a gold coin originally purchased for $1 by her great-grandfather 50 years ago. Today the coin is worth $450. The rate of return realized on the sale of this coin is approximately equal to: Pick the closest answer.

13%

If you earn 3% compounded semiannually on your deposit of $200, it will take approximately_______ years before you have $300. Pick the closest answer.

13.6

Megan owns stock in a company which has consistently paid a growing dividend over the last five years. At the end of the first year Megan owned the stock, she received $1.71 per share and at the end of the fifth year, she received $2.89 per share. What is the growth rate of the dividends during this time? Pick the closest answer.

14%

Suppose you receive $3,000 a year in Years One through Four, $4,000 a year in Years Five through Nine, and $2,000 in Year 10, with all the money to be received at the end of the year. If your discount rate is 12%, what is the present value of these cash flows? Pick the closest answer.

18,926.12

If you have an account with a 21.5% annual percentage rate where interest is compounded quarterly, what is the effective annual rate of interest? Pick the closest answer.

23.3%

Your subscription to Consumer Reports is about to expire. You may renew it for $24 a year or, instead, you may get a lifetime subscription to the magazine for a onetime payment of $403 today. Payments for the regular subscription are made at the beginning of each year. Using a discount rate of 5%, how many years does it take to make the lifetime subscription the better deal? Pick the closest answer.

33 years

Larry deposited $5,000 in a savings account that paid 8% interest compounded quarterly. What is the effective annual rate of interest?

8.24%

If a savings bond can be purchased today for $29.50 and has a maturity value at the end of 25 years of $100, what is the annual rate of return on the bond? Pick the closest answer.

5%

In 1976, the average price of a domestic car was $5,100. Twenty years later, in 1996, the average price was $16,600. What was the annual growth rate in the car price over the 20-year period? Pick the closest answer.

6.07%

In 1983, the average tuition for one year in the MBA program at a university was $3,600. Thirty years later, in 2013, the average tuition was $27,400. What is the compound annual growth rate in tuition (rounded to the nearest whole percentage) over the 30-year period? Pick the closest

7%

Your college has agreed to give you a $10,000 tuition loan. As part of the agreement, you must repay $12,600 at the end of the three-year period. What interest rate is the college charging?

8%

Consolidated Freightways is financing a new truck with a loan of $60,000 to be repaid in six annual end-ofyear installments of $13,375. What annual interest rate is Consolidated Freightways paying? Pick the closest

9%

An annuity due may also be referred to as a deferred annuity.

False

An ordinary annuity exists when the equal payments occur at the beginning of each time period.

False

Money has a time value so long as interest is earned by saving or investing money.

True

Which of the following terms best describes an annuity due?

Payment at beginning of year

The ________ value of a savings or investment is its amount or value at the current times.

Present

A famous athlete is awarded a contract that stipulates equal payments to be made at the end of each month over a period of five years. To determine the value of the contact today, you would need to use:

Present value of an ordinary annuity

The time value concept/calculation used in amortizing a loan is

Present value of annuity

If the stated or nominal interest rate is 10 percent and the inflation rate is 4 percent, the net or differential compounding rate would be _______ percent.

Six

Select ALL of the following statements that are false

The effective annual rate is determined by multiplying the interest rate charged per period by the number of periods in a year

Select ALL of the following statements that are not descriptive of an amortization schedule?

The same dollar amount of interest is paid with each payment

$1000 deposited in a bank that earns 7% per year will become approximately $7,600 is 30 years.

True

A fixed-rate mortgage is an example of an annuity.

True

A loan amortization schedule shows the breakdown of each payment between interest and principal, as well as the remaining balance after each payment.

True

An amortized loan is repaid in equal payments over a specified time period.

True

An annuity is a series of equal payments that occur over a number of time periods.

True

As the interest rate increases, present value decreases.

True

At a zero interest rate, the present value of $1 remains at $1 and is not affected by time.

True

At very low interest rates, the "Rule of 72" does not approximate the compounding process well.

True

The Rule of 72 is an estimate of how long it would take to double a sum of money at a given interest rate.

True

The effective annual rate (EAR) is sometimes called the annual effective yield.

True

The effective annual rate (EAR) is the true opportunity cost measure of the interest rate.

True

The method of calculating the annual percentage rate (APR) is set by law.

True

A loan that is repaid in equal payments over a specified time period is called a(n)

amortized loan

A loan that is repaid in equal payments over a specified time period is referred to as a(n):

amortized loan

A series of equal payments or receipts that occur at the beginning of each of a number of time periods is referred to as:

an annuity due

The interest rate determined by multiplying the interest rate charged per period by the number of periods in a year is called the:

annual percentage rate

In future value or present value problems, unless stated otherwise, cash flows are assumed to be

at the end of a time period

When the amount earned on a deposit becomes part of the principal at the end of a period and can earn a return in future periods, this is called

compound interest

The future value of a dollar_____ as the interest rate increases and its future value ______ the farther in the future is the funds are to be received.

increases; increases

You need to have $35,000 on hand to buy a new Lexus five years from today. To achieve that goal, you want to know how much you must invest today in a certificate of deposit guaranteed to return you 3% per year. To help determine how much to investment today, you will use:

present value of a single lump sum

Interest earned only on an investment's principal or original amount is referred to as:

simple interest

Suppose you have a choice of two equally risk annuities, each paying $1,000 per year for 20 years. One is an annuity due, while the other is an ordinary annuity. Which annuity should you choose?

the annuity due

The method of calculating interest on loan that is set by law is called the:

Annual percentage rate (APR)

If you will receive $100 per year with the first payment one year from now for a period of three years with a 12% discount rate, what would be the value of your investment today? Pick the closest answer.

$240

An investment will mature in 20 years. Its maturity value is $1,000. If the discount rate is 7%, what is the present value of the investment? Pick the closest answer.

$258

The present value of an annuity of $5,000 to be received at the end of each of the 6 years at a discount rate of 4% would be: (Pick the closest answer.)

$26,211

The present value of an annuity of $5,000 to be received at the beginning of each of the 6 years at a discount rate of 4% would be: Pick the closest answer

$27,259

An ordinary annuity of $5,000 invested at 8% in 5 years would result in a future value of (Pick the closest answer.):

$29,333

Suppose you were going to save $1,000 per year for three years at a 10% interest rate compounded annually, with the first investment occurring today. What would be the future value of this investment? Pick the closest answer.

$3,641

You borrow $10,000 to pay for your college tuition. The loan is amortized over a three-year period with an interest rate of 18%. The payments are made at the end of each year. What is your remaining balance at the end of Year Two? Pick the closest answer

$3,898

You need $8,000 four years from now for a down payment on your future house. How much money must you deposit today if your credit union pays 5% interest compounded annually? Pick the closest answer.

$6,581.62

Gavin deposits $5,000 in a five-year certificate of deposit paying 6% compounded semi-annually. How much will Gavin have at the end of the five-year period? Pick the closest answer.

$6,720

It will take approximately 9.6 years for a $100 deposit to result in a future value of $600 if you can earn 10% on your deposit,

False

Level cash flow amounts that occur at the end of each period, starting at the end of the first period, are an annuity due.

False

Simple interest is interest earned on the investment's principal and subsequently- earned interest.

False

The annual percentage rate (APR) overstates the true or effective interest cost.

False

The annual percentage rate is the true opportunity cost measure of the interest rate.

False

The effective annual rate is determined by multiplying the interest rate charged per period by the number of periods in a year.

False

The future value of $100 deposited today for 10 years at 10% compounded annually is $38.55.

False

The future value of a $100 ordinary annuity deposited for 10 years at 10% is $614.46

False

The interest portion increases and the principal portion decreases over time under a typical loan amortization schedule.

False

The present value of $100 received in 10 years at 10% is $259.37.

False

The present value of a $100 ordinary annuity deposited for 10 years at 10% is $1,593.74.

False

The return provided by a $100 ordinary annuity deposited for 10 years that results in a future value of $1,593.74 is 15%.

False

With compound interest, interest is earned only on the investment's principal.

False

Your current bank is paying 6.25% simple interest rate. You can move your savings account to Harris Bank that pays 6.25% compounded annually or to First Chicago bank paying 6% compounded semi-annually. To maximize your return you would choose:

Harris Bank

Discounting in an arithmetic process whereby a future sum decreases at a compounding interest rate over time to reach a present value.

True

For the same annual percentage rate, more frequent compounding increases the future value of an investor's funds more quickly.

True

If the compound inflation rate were greater than the compound interest rate, future purchasing power on our savings would fall.

True

It will take approximately 18.8 years for a $100 deposit to grow to $600 if you can earn 10% on your deposit.

True

The future value of $100 deposited today for years at 10% compounded annually is $259.37

True

The future value of a $100 ordinary annuity deposited for 10 years at 10% is $1,593.74.

True

The present value of $100 ordinary annuity deposited for 10 years at 10% is $614.46.

True

The present value of $100 received in 10 years at 10% compounded annually is $38.55.

True

The return provided by $100 deposited today for 10 years that results in a future value of $614.46 is 19.91%.

True

The return provided by a $100 ordinary annuity deposited for 10 years that results in a future value of $614.46 is negative 11.45%.

True

The interest rate that measures the true interest rate when compounding occurs more frequently than once a year is called the:

effective annual rate

Select ALL of the following statements that are true.

-The present value of a future sum decreases as the discount rate increases. - If the present value of a sum is equal to its future value, the interest rate must be zero -If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series

Compounding means that interest earned each year, plus the principal, will be reinvested at the stated rate.

True

The return provided by a$100 ordinary annuity deposited for 10 years that results in a future value of $1,593.74 is 10%.

True

When the annual interest rate stays the same, more frequent interest compounding helps savers earn more interest over the course of the year.

True

You have just won a lottery! You will receive $50,000 a year beginning one year from now for 20 years. If your required rate of return is 10%, what is the present value of your winning lottery ticket? Pick the closest answer

$425,700

When compounding more than once a year, the true opportunity costs measure of the interest rate is indicated by the:

Effective annual rate

As the number of periods increases, present value increases.

False

At very high interest rates the "Rule of 72" will result in a small estimation error for estimate of the time for an investment to double.

False

Because interest compounds, the annual percentage rate formula will overstate the true interest cost of a loan.

False

For a given discount rate, an ordinary annuity and an annuity due have the same present value.

False

If the interest rate is 0% for 10 years, then the present value will be less than the future value.

False

If you earn 3% on your deposit of $500, it will take approximately 9 years before you have $550.

False

Compound interest is interest earned on interest in addition to interest earned on principal.

True