Finance Exam 2 Ch. 5

The effective rate of interest and compounding frequency are inversely related.

False

The effective rate of interest is the contractual rate of interest charged by a lender or promised by a borrower.

False

The annual percentage rate (APR) is the nominal rate of interest, found by multiplying the periodic rate by the number of periods in one year.

True

The annual percentage yield (APY) is the effective rate of interest that must be disclosed to customers by banks on their savings products as a result of "truth in savings laws."

True

The effective annual rate increases with increasing compounding frequency.

True

The effective rate of interest differs from the nominal rate of interest in that it reflects the impact of compounding frequency.

True

The nominal and effective rates are equivalent for annual compounding.

True

A beach house in Southern California now costs $350,000. Inflation is expected to cause this price to increase at 5 percent per year over the next 20 years before Eric and Karinna retire from successful careers in commercial art. 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 beach house upon retirement?

$11,472

Entertainer's Aid plans five annual colossal concerts, each in a different nation's capital. The concerts will raise funds for an endowment which would provide the World Wide Hunger Fund with $3,000,000 per year into perpetuity. The endowment will be given at the end of the fifth year. The rate of interest is expected to be 9 percent in all future periods. How much must Entertainer's Aid deposit each year to accumulate to the required amount?

$5,569,749

Calculate the future value of $4,600 received today if it is deposited at 9 percent for three years.

$5,957

Nico establishes a seven-year, 8 percent loan with a bank requiring annual end-of-year payments of $960.43. Calculate the original principal amount.

$5000

A firm wishes to establish a fund which, in 10 years, will accumulate to $10,000,000. The fund will be used to repay an outstanding bond issue. The firm plans to make deposits, which will earn 12 percent, to this fund at the end of each of the 10 years prior to maturity of the bond. How large must these deposits be to accumulate to $10,000,000?

$569,833.04

Otto is planning for his son's college education to begin ten years from today. He estimates the end-of-the-year tuition, books, and living expenses to be $10,000 per year for a four-year degree. How much must Otto deposit today, at an interest rate of 12 percent, for his son to be able to withdraw $10,000 per year for four years of college?

$9780

How many years would it take for Jughead to save an adequate amount for retirement if he deposits $2,000 per month into an account beginning today that pays 12 percent per year if he wishes to have a total of $1,000,000 at retirement?

15 years

You have been given the opportunity to earn $20,000 five years from now if you invest $9,524 today. What will be the rate of return to your investment?

16 percent

What annual rate of return would Jia need to earn if she deposits $20,000 per year into an account beginning one year from today in order to have a total of $1,000,000 in 30 years?

3.3 percent

A wealthy art collector has decided to endow her favorite art museum by establishing funds for an endowment which would provide the museum with $1,000,000 per year for acquisitions into perpetuity. The art collector will give 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 6 percent in all future periods. How much must the art collector deposit each year to accumulate to the required amount?

$1,264,466

The New York Soccer Association would like to accumulate $10,000 by the end of 4 years from now to finance a big soccer weekend for its members. The Association currently has $2,500 and wishes to raise the balance by arranging annual fund-raising events. How much money should they raise at each annual fund-raising event assuming 8 percent rate of interest?

$1,464.41

China Manufacturing Agents, Inc. is preparing a five-year plan. Today, sales are $1,000,000. If the growth rate in sales is projected to be 10 percent over the next five years, what will the dollar amount of sales be in year five?

$1,610,510

Calculate the present value of $800 received at the beginning of year 1, $400 received at the beginning of year 2, and $700 received at the beginning of year 3, assuming an opportunity cost of 9 percent.

$1,756.15

Suzy wants to buy a house but does not want to get a loan. The average price of her dream house is $500,000 and its price is growing at 5 percent per year. How much should Suzy invest in a project at the end of each year for the next 5 years in order to accumulate enough money to buy her dream house with cash at the end of the fifth year? Assume the project pays 12 percent rate of return.

$100,450

Dan and Jia are newlyweds and have just purchased a condominium for $70,000. Since the condo is very small, they hope to move into a single-family house in 5 years. How much will their condo worth in 5 years if inflation is expected to be 8 percent?

$102,853

Thelma is planning for her son's college education to begin five years from today. She estimates the yearly tuition, books, and living expenses to be $5,000 per year for a four-year degree, assuming the expenses incur only at the end of the year. How much must Thelma 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?

$11,270

The future value of an ordinary annuity of $1,000 each year for 10 years, deposited at 3 percent, is ________.

$11,464

Danny Joe borrows $10,500 from the bank at 11 percent annually compounded interest to be repaid in six equal annual installments. The interest paid in the first year is ________.

$1155

The present value of an ordinary annuity of $2,350 each year for eight years, assuming an opportunity cost of 11 percent, is ________.

$12,093

Aunt Butch borrows $19,500 from the bank at 8 percent annually compounded interest to be repaid in 10 equal annual installments. The interest paid in the third year is ________.

$1336

Rita borrows $4,500 from the bank at 9 percent annually compounded interest to be repaid in three equal annual installments. The interest paid in the third year is ________.

$147

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

$17,460

A ski chalet at Peak n' Peak now costs $250,000. Inflation is expected to cause this price to increase at 5 percent per year over the next 10 years before Chris and Julie 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?

$22,109

To pay for her college education, Gina is saving $2,000 at the beginning of each year for the next eight years in a bank account paying 12 percent interest. How much will Gina have in that account at the end of 8th year?

$27,552

The present value of a $20,000 perpetuity at a 7 percent discount rate is ________.

$285,714

Xiao Li wishes to accumulate $50,000 by the end of 10 years by making equal annual end-of-year deposits over the next 10 years. If Xiao Li can earn 5 percent on her investments, how much must she deposit at the end of each year?

$3975

Janice borrows $25,000 from the bank at 15 percent to be repaid in 10 equal annual installments. Calculate the end-of-year payment.

$4,981.30

Aunt Tilly borrows $3,500 from the bank at 12 percent annually compounded interest to be repaid in four equal annual installments. The interest paid in the first year is ________.

$420

Marc has purchased a new car for $15,000. He paid $2,500 as down payment and he paid the balance by a loan from his hometown bank. The loan is to be paid on a monthly basis for two years charging 12 percent interest. How much are the monthly payments?

$588.42

Find the equal annual end-of-year payment on $50,000, 15 year, and 10 percent loan.

$6,573.69

Dottie has decided to set up an account that will pay her granddaughter (Lexi) $5,000 a year indefinitely. How much should Dottie deposit in an account paying 8 percent annual interest?

$62,500

Xiao Xin is planning to accumulate $40,000 by the end of 5 years by making 5 equal annual deposits. If she plans to make her first deposit today and can earn an annual compound rate of 9 percent on her investment, how much must each deposit be in order to accumulate the $40,000?

$6684

Mary will receive $12,000 per year for the next 10 years as royalty for her work on a finance book. What is the present value of her royalty income if the opportunity cost is 12 percent?

$67,800

The future value of a $10,000 annuity due deposited at 12 percent compounded annually for each of the next 5 years is ________.

$71,152

$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 these cash flows are deposited at 12 percent, their combined future value at the end of year 3 is ________.

$727

Ashley owns stock in a company which has consistently paid a growing dividend over the last five years. The first year Ashley owned the stock, she received $1.71 per share and in the fifth year, she received $2.89 per share. What is the growth rate of the dividends over the last five years?

11 percent

Dorothy borrows $10,000 from the bank. For a four-year loan, the bank requires annual end-of-year payments of $3,223.73. The annual interest rate on the loan is ________.

11 percent

How long would it take for you to save an adequate amount for retirement if you deposit $40,000 per year into an account beginning today that pays 12 percent per year if you wish to have a total of $1,000,000 at retirement?

11.5 years

A local brokerage firm is offering a zero-coupon certificate of deposit for $10,000. At maturity, three years from now, the investor will receive $14,000. What is the rate of return on this investment?

12 percent

John borrowed $12,000 to buy a new car and expects to pay $564.87 per month for the next 2 years to pay off the loan. What is the loan's rate of interest?

12 percent

Timothy borrows $6,930 from the bank. For a four-year loan, the bank requires annual end-of-year payments of $2,281.86. Calculate the interest rate on the loan.

12 percent

How long would it take for Nico to save an adequate amount for retirement if he deposits $40,000 per year into an account beginning one year from today that pays 12 percent per year if he wishes to have a total of $1,000,000 at retirement?

12.2 years

What is the rate of return on an investment of $16,278 if the company expects to receive $3,000 per year for the next 10 years?

13 percent

What annual rate of return would Grandma Zoe need to earn if she deposits $1,000 per month into an account beginning one month from today in order to have a total of $1,000,000 in 30 years?

5.98 percent

A deep-discount bond can be purchased for $312 and in 20 years it will be worth $1,000. What is the rate of interest on the bond?

6 percent

What effective annual rate of return (EAR) would Rayne need to earn if she deposits $1,000 per month into an account beginning one month from today in order to have a total of $1,000,000 in 30 years?

6.14 percent

Detta borrows $20,000 from the bank. For a five-year loan, the bank requires annual end-of-year payments of $4,878.05. The annual interest rate on the loan is ________.

7 percent

The rate of return earned on an investment of $50,000 today that guarantees an annuity of $10,489 for six years is approximately ________.

7 percent

What is the rate of return on an investment of $124,090 if the company expects to receive $10,000 per year for the next 30 years?

7 percent

If a United States Savings bond can be purchased for $14.60 and has a maturity value at the end of 25 years of $100, what is the annual rate of return on the bond?

8 percent

A local bank is offering a zero-coupon certificate of deposit for $25,000. At maturity, three years from now, the investor will receive $32,000. What is the rate of return on this investment?

9 percent

Alexis owns stock in a company which has consistently paid a growing dividend over the last 10 years. The first year Alexis owned the stock, she received $4.50 per share and in the 10th year, she received $4.92 per share. What is the growth rate of the dividends over the last 10 years?

9.3 percent

Which of the following is true of annuities? A) An ordinary annuity is an equal payment paid or received at the beginning of each period. B) An annuity due is a payment paid or received at the beginning of each period that increases by an equal amount each period. C) An annuity due is an equal stream of cash flows is paid or received at the beginning of each period. D) An ordinary annuity is an equal payment paid or received at the end of each period that increases by an equal amount each period.

C) An annuity due is an equal stream of cash flows is paid or received at the beginning of each period.

If the present value of a perpetual income stream is increasing, the discount rate must be ________.

Decreasing

The annual rate of return is referred to as the ________.

Discount rate

The rate of interest actually paid or earned, also called the annual percentage rate (APR), is the ________ interest rate.

Effective

An ordinary annuity is an annuity in which cash flows occur at the beginning of each period.

False

The future value of a dollar ________ as the interest rate increases and ________ the further in the future an initial deposit is to be received.

Increases; Increases

A(n) ________ is an annuity with an infinite life making continual annual payments.

Perpetuity

An annuity with an infinite life is called a(n) ________.

Perpetuity

The amount of money that would have to be invested today at a given interest rate over a specified period in order to equal a future amount is called ________.

Present value

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

Present value of an annuity

An annuity due is an amount that occur at the beginning of each period.

True

.Calculate the present value of an annuity of $3,900 each year for four years, assuming an opportunity cost of 10 percent.

$12,363

.Calculate the present value of $89,000 to be received in 15 years, assuming an opportunity cost of 14 percent.

$12,469

Calculate the future value of $6,490 received today and deposited for five years in an account which pays interest of 14 percent compounded semiannually.

$12,766

If you expect to retire in 30 years, live on $50,000 per year and expect the inflation to average 3% over the next 30 years, what amount of annual income will you need to live at the same comfort level in 30 years?

$121,363

The future value of $100 received today and deposited at 6 percent for four years is ________.

$126

The future value of $100 received today and deposited in an account for four years paying semiannual interest of 6 percent is ________.

$127

The present value of $200 to be received 10 years from today, assuming an opportunity cost of 10 percent, is ________.

$77

$1,200 is received at the beginning of year 1, $2,200 is received at the beginning of year 2, and $3,300 is received at the beginning of year 3. If these cash flows are deposited at 12 percent, their combined future value at the end of year 3 is ________.

$8142

Everything else being equal, the higher the interest rate, the higher the future value.

True

Everything else being equal, the longer the period of time, the lower the present value.

True

For a given positive interest rate, the future value of $100 increases with the passage of time. Thus, the longer the period of time, the greater the future value.

True

Future value increases with increases in the interest rate or the period of time funds are left on deposit.

True

In general, with an amortized loan, the payment amount remains constant over the life of the loan, the principal portion of each payment grows over the life of the loan, and the interest portion of each payment declines over the life of the loan.

True

The future value of an annuity due is always greater than the future value of an otherwise identical ordinary annuity for interest rates greater than zero.

True

When computing an interest or growth rate, the rate will increase with an increase in future value, holding present value and the number of periods constant.

True

A wealthy industrialist wishes to establish a $2,000,000 trust fund which will provide income for his grandchild into perpetuity. He stipulates in the trust agreement that the principal may not be distributed. The grandchild may only receive the interest earned. If the interest rate earned on the trust is expected to be at least 7 percent in all future periods, how much income will the grandchild receive each year?

$140,000

Bill 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 Bill can earn 12 percent on his contributions, how much will he have at the end of the twentieth year?

$144,104

Adam borrows $4,500 at 12 percent annually compounded interest to be repaid in four equal annual installments. The actual end-of-year payment is ________.

$1482

Nico 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 ________.

$15,000

Jia borrows $50,000 at 10 percent annually compounded interest to be repaid in four equal annual installments. The actual end-of-year loan payment is ________.

$15,773

The present value of an ordinary annuity of $350 each year for five years, assuming an opportunity cost of 4 percent, is ________.

$1558

Calculate the present value of $5,800 received at the end of year 1, $6,400 received at the end of year 2, and $8,700 at the end of year 3, assuming an opportunity cost of 13 percent.

$16,174.42

Calculate the present value of a $10,000 perpetuity at a 6 percent discount rate.

$166,667

The present value of a $25,000 perpetuity at a 14 percent discount rate is ________.

$178,571

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

$190,000

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

$20,157

Calculate the future value of $10,000 received today and deposited for six years in an account which pays interest of 12 percent compounded quarterly.

$20,328

Janice would like to send her parents on a cruise for their 25th wedding anniversary. She has priced the cruise at $15,000, and she has 5 years to accumulate this money. How much must Janice deposit annually in an account paying 10 percent interest in order to have enough money to send her parents on the cruise?

$2457

Hayley makes annual end-of-year payments of $6,260.96 on a five-year loan with an 8 percent interest rate. The original principal amount was ________.

$25,000

The future value of $200 received today and deposited at 8 percent for three years is ________.

$252

The future value of $200 received today and deposited at 8 percent compounded semiannually for three years is ________.

$253

The future value of $200 received today and deposited for three years in an account which pays semiannual interest of 8 percent is ________.

$253

You have been offered a project paying $300 at the beginning of each year for the next 20 years. What is the maximum amount of money you would invest in this project if you expect 9 percent rate of return to your investment?

$2985

A generous benefactor to a local ballet plans to make a one-time endowment that would provide the ballet 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?

$3,000,000

A generous philanthropist plans to make a one-time endowment to a renowned heart research center which would provide the facility with $250,000 per year into perpetuity. The rate of interest is expected to be 8 percent for all future time periods. How large must the endowment be?

$3,125,000

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 ________.

$3044

The future value of a $2,000 annuity due deposited at 8 percent compounded annually for each of the next 10 years is ________.

$31,291

Dan 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 Dan can earn 10 percent on his contributions, how much will he have at the end of the tenth year?

$31,874

The future value of an ordinary annuity of $2,000 each year for 10 years, deposited at 12 percent, is ________.

$35,098

The present value of $100 to be received 10 years from today, assuming an opportunity cost of 9 percent, is ________.

$42

How much would Sophie have in her account at the end of 10 years if she deposit $2,000 into the account today if she earned 8 percent interest and interest is compounded continuously?

$4451

The present value of $100 received at the end of year 1, $200 received at the end of year 2, and $300 received at the end of year 3, assuming an opportunity cost of 13 percent, is ________.

$453

Calculate the future value of an annuity of $5,000 each year for eight years, deposited at 6 percent.

$49,487.34

The future value of an annuity of $1,000 each quarter for 10 years, deposited at 12 percent compounded quarterly is ________.

$75,401

Calculate the combined future value at the end of year 3 of $1,000 received at the end of year 1, $3,000 received at the end of year 2, and $5,000 received at the end of year 3, all sums deposited at 5 percent.

$9252

James plans to fund his individual retirement account, beginning today, with 20 annual deposits of $2,000, which he will continue for the next 20 years. If he can earn an annual compound rate of 8 percent on his deposits, the amount in the account upon retirement will be ________.

$98,846

What is the highest effective rate attainable with a 12 percent nominal rate?

12.75%

Julian was given a gold coin originally purchased for $1 by his 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 ________.

13 percent

If a United States Savings bond can be purchased for $29.50 and has a maturity value of $100 at the end of 25 years, what is the annual rate of return on the bond?

5 percent

In comparing an ordinary annuity and an annuity due, which of the following is true? A) The future value of an annuity due is always greater than the future value of an otherwise identical ordinary annuity. B) The future value of an ordinary annuity is always greater than the future value of an otherwise identical annuity due. C) The future value of an annuity due is always less than the future value of an otherwise identical ordinary annuity, since one less payment is received with an annuity due. D) All things being equal, one would prefer to receive an ordinary annuity compared to an annuity due.

A) The future value of an annuity due is always greater than the future value of an otherwise identical ordinary annuity.

Assume Julian has a choice between two deposit accounts. Account A has an annual percentage rate of 7.55 percent but with interest compounded monthly. Account B has an annual percentage rate of 7.45 percent with interest compounded continuously. Which account provides the highest effective annual return?

Account A

________ is the amount earned on a deposit that has become the part of the principal at the end of a specified time period.

Compound interest

Everything else being equal, the higher the discount rate, the higher the present value.

False

For any interest rate and for any period of time, the more frequently interest is compounded, the greater the amount of money that has to be invested today in order to accumulate a given future amount.

False

Future value is the value of a future amount at the present time, found by applying compound interest over a specified period of time.

False

In general, with an amortized loan, the payment amount grows over the life of the loan, the principal portion of each payment grows over the life of the loan, and the interest portion declines over the life of the loan.

False

In general, with an amortized loan, the payment amount remains constant over the life of the loan, both the principal portion of and the interest portion declines over the life of the loan.

False

In general, with an amortized loan, the payment amount remains constant over the life of the loan, the principal portion of each payment declines over the life of the loan, and the interest portion of each payment grows over the life of the loan.

False

Since individuals are always confronted with opportunities to earn positive rates of return on their funds, the timing of cash flows does not have any significant economic consequences.

False

The greater the interest rate and the longer the period of time, the higher the present value.

False

The nominal (stated) annual rate is the rate of interest actually paid or earned.

False

Time value of money is based on the belief that a dollar that will be received at some future date is worth more than a dollar today.

False

When computing an interest or growth rate, the rate will decrease with an increase in future value, holding present value and the number of periods constant.

False

When computing an interest or growth rate, the rate will increase with a decrease in future value, holding present value and the number of periods constant.

False

When computing the number of deposits needed to accumulate a future sum, it will take longer if the interest rates are higher, holding the future value and deposit size constant.

False

The rate of interest agreed upon contractually charged by a lender or promised by a borrower is the ________ interest rate.

Nominal

.When computing the number of deposits needed to accumulate to a future sum, it will take longer if the interest rate decreases, holding the future value and deposit size constant.

True