FINC 409 - Chapter 9 - Practice Problems

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

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

True

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

True

Discounting is 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 I can earn 10% on my deposit.

True

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

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 future value of a $100 deposit in 10 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 method of calculating the annual percentage rate (APR) is set by law.

True

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

True

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

True

The return provided by $100 deposited 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 $1,593.74 is 10%.

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

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

True

If we will receive $100 per year beginning one year from now for a period of three years with a 12% discount rate, what would be the value of our investment today? Pick the closest answer. a. $230 b. $240 c. $250 d. $260

b. $240 END mode PMT 100 FV 0 N 3 I/Y 12 → PV = $240.18

Multiple Answer Question: 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. a. present value (PV) b. future value (FV) c. interest rate (I/Y) d. inflation rate (I) e. number of periods (N) f. payments (PMT)

b, d, f

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. a. $1,200.50 b. $1,220.20 c. $1,174.80 d. $1,217.50

b. $1,220.20

$2,000 invested today at 6% in 3 years would result in a future value of (Pick the closest answer): a. $2,000 b. $2,382 c. $6,362 d. none of the above

b. $2,382 PV -2,000 N 3 I/Y 6 → FV = $2,382.03

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

False

It will take approximately 9.6 years for a $100 deposit to result in a future value of $600 if I can earn 10% on my 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 a $100 deposit in 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 a $100 deposit 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 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. a. 33 years b. 28 years c. 36 years d. 40 years

A. 33 years BGN mode PV 403 FV 0 PMT -24 I/Y 5 → N = 32.9 → 33 years Check: FV 0 PMT -24 I/Y 5 N 33 → PV = $403.26 FV 0 PMT -24 I/Y 5 N 33 → PV = $403.26

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

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 the 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 I earn 3% on my deposit of $500, it will take 9 years before I have $550.

False

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. a. $1,254 b. $1,210 c. $1,188 d. $1,160

a. $1,254 PV 1,000 N 2 I/Y 12 → FV = $1,254.40

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%, how much are you willing to lend now? Pick the closest answer. a. $1,502 b. $1,786 c. $1,802 d. $1,818

a. $1,502

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.): a. $26,210 b. $33,165 c. $3,950 d. none of the above

a. $26,210 END mode PMT +5,000 FV 0 N 6 I/Y 4→ PV = -$26,210.68

Tracey deposits $5,000 in a five-year certificate of deposit paying 6% compounded semi-annually. How much will Tracey have at the end of the five-year period? Pick the closest answer. a. $6,720 b. $6,690 c. $6,596 d. $6,910

a. $6,720 PV 5,000 I/Y 3 N 10 → FV = $6,719.58

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 answer. a. 10% b. 10.6% c. 11% d. 11.2%

a. 10%

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. a. 18,926.12 b. 19,560.80 c. 20,651.24 d. 24,175.00

a. 18,926.12

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? a. 8% b. 9% c. 11% d. 6%

a. 8%

Multiple Answer Question: Select ALL of the following statements that are true. a. The present value of a future sum decreases as the discount rate increases. b. If the present value of a sum is equal to its future value, the interest rate must be zero. c. 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. d. For a given APR, the present value of a future sum decreases as the number of discounting periods per year decreases.

a. The present value of a future sum decreases as the discount rate increases. b. If the present value of a sum is equal to its future value, the interest rate must be zero. c. 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.

The interest rate determined by multiplying the interest rate charged per period by the number of periods in a year is called the: a. annual percentage rate b. compound rate of interest c. stated rate of interest d. effective annual rate

a. annual percentage rate

The _________ value of a savings or investment is its amount or value at the current time. a. present b. future c. book d. none of the above

a. present

Multiple Answer Question: 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. a. present value (PV) b. future value (FV) c. interest rate (I/Y) d. inflation rate (I) e. number of periods (N) f. payments (PMT) g. begin/end mode (BGN/END)

a. present value (PV) b. future value (FV) c. interest rate (I/Y) e. number of periods (N)

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: a. present value of a single lump sum b. future value of a single lump sum c. present value of an annuity d. future value of an annuity

a. present value of a single lump sum

Interest earned only on an investment's principal or original amount is referred to as: a. simple interest b. compound interest c. discount interest d. annuity interest

a. simple interest

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. a. $178 b. $258 c. $276 d. $362

b. $258 V 1,000 N 20 I/Y 7 → PV = $258.42

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. a. $26,210 b. $27,259 c. $17,326 d. $18,365

b. $27,259 BGN mode PMT 5,000 N 6 I/Y 4 FV 0 → PV = -$27,259.11

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. a. $418,250 b. $425,700 c. $444,640 d. $453,850

b. $425,700 END mode PMT 50,000 N 20 I/Y 10 FV 0 → PV = $425,678.19

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. a. $6,269.59 b. $6,581.62 c. $6,394.12 d. $6,189.83

b. $6,581.62 FV 8,000 N 4 I/Y 5 → PV = $6,581.62

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. a. $67,520 b. $73,572 c. $81,990 d. $75,686

b. $73,572

Kristen has just purchased a used Mercedes for $18,995. She plans to make a $2,500 down payment on the new car. What is the amount of her monthly payment on the remaining loan if she must pay 12% annual interest on a 24-month car loan? Pick the closest answer. a. $759.53 b. $776.48 c. $894.16 d. $899.87

b. $776.48

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. You can presently invest in high-yield bonds earning a compound annual rate 14% per year. How much must you invest at the end of each of the next seven years to be able to purchase your dream car in seven years? Pick the closest answer. a. $8,831.46 b. $9,080.20 c. $9,125.42 d. $9,282.09

b. $9,080.20

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. a. 23.75% b. 23.3% c. 21.5% d. none of the above

b. 23.3% INTEREST PER QUARTER= 𝟐𝟏.𝟓 = 𝟓. 𝟑𝟕𝟓% → EAR = (1 + 0.05375)4 - 1 = 1.23296 -1 = 23.3%

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. a. 5.89% b. 6.07% c. 7.12% d. 8.23%

b. 6.07% PV 5,100 FV -16,600 N 20 → I/Y = 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 answer. a. 6% b. 7% c. 8% d. 10%

b. 7%

Larry deposited $5,000 in a savings account that paid 8% interest compounded quarterly. What is the effective rate of interest? a. 8.00% b. 8.24% c. 8.33% d. 8.46%

b. 8.24%

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: a. your current bank b. Harris Bank c. First Chicago bank d. you are indifferent, because the effective interest rate for all three banks is the same

b. Harris Bank

Multiple Answer Question: Select ALL of the following statements that are not descriptive of an amortization schedule? a. Each payment is the same. b. The same dollar amount of interest is paid with each payment. c. Payment on principal increases with each total payment. d. Balance owed is reduced by each payment.

b. The same dollar amount of interest is paid with each payment.

A loan that is repaid in equal payments over a specified time period is referred to as a (n): a. discounted loan b. amortized loan c. simple interest-free loan d. inflation-indexed loan

b. amortized loan

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 a. ten b. six c. four d. fourteen

b. six

Suppose you have a choice of two equally risky annuities, each paying $1,000 per year for 20 years. One is an annuity due, while the other is an ordinary annuity. Which annuity would you choose? a. the ordinary annuity b. the annuity due c. either one because the annuities have the same present value d. without information about the appropriate interest rate, we cannot tell which annuity is better

b. the annuity due

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 each year? Pick the closest answer. a. $8,042 b. $9,026 c. $10,053 d. $11,120

c. $10,053 END mode PV 25,000 FV 0 N 3 I/Y 10 → PMT = $10,052.87

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. a. $2,914 b. $2,938 c. $2,972 d. $2,999

c. $2,972 PV 2,000 N 20 I/Y 2 → FV = $2,971.89

The future value of an ordinary annuity of $5,000 invested at 8% in 5 years would result in a value of (Pick the closest answer.): a. $25,000 b. $7,345 c. $29,335 d. none of the above

c. $29,335 END mode PMT -5,000 PV 0 N 5 I/Y 8 → FV = $29,333.00

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. a. $2,124 b. $2,310 c. $3,641 d. $3,812

c. $3,641 BGN mode PMT -1,000 N 3 I/Y 10 PV 0 → FV = $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%. What is your remaining balance at the end of Year Two? Pick the closest answer. a. $7,201 b. $4,599 c. $3,898 d. $3,303

c. $3,898 PV 10,000 FV 0 I/Y 18 N 3 → PMT = $4,599.24 YR1: INT = 18%(10,000) = $1,800 → PRIN = 4,599.24 - 1,800 = $2,799.24 END BAL = 10,000 - 2,799.24 = $7,200.76 YR2: INT = 7,200.76(0.18) = $1,296.14 → PRIN 4,599.24 - 1,296.14 = $3,303.10 END BAL 7,200.76 - 3,303.10 = $3,897.66

Taylor has just accepted a job as a stockbroker. He estimates his gross pay each year for the next three years is $35,000 in year 1, $21,000 in year 2, and $32,000 in year 3. The present value of these cash flows, if they are discounted at 4%, is closest to a. $79,452.30 b. $80,294.50 c. $81,517.10 d. $88,000

c. $81,517.10

You deposit $1,000 in a long-term certificate of deposit with an interest rate of 9%. How many years will it take for you to triple your deposit? Pick the closest answer. a. 11 years b. 12 years c. 13 years d. 14 years

c. 13 years PV -1,000 FV 3,000 I/Y 8.81 → N = 13.01

Consolidated Freightways is financing a new truck with a loan of $60,000 to be repaid in six annual end-of-year installments of $13,375. What annual interest rate is Consolidated Freightways paying? Pick the closest answer. a. 7% b. 8% c. 9% d. 10%

c. 9% END mode PV 60,000 PMT -13,375 N 6 FV 0 → I/Y = 9%

Multiple Answer Question: Select ALL of the following statements that are false. a. For a given APR, more frequent compounding results in additional return on the investment. b. An amortized loan is repaid in equal payments over a specified time period. c. The effective annual rate is determined by multiplying the interest rate charged per period by the number of periods in a year. d. Each of the above statements is true.

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

A loan that is repaid in equal payments over a specified time period is called a (n) a. discount loan b. balloon loan c. amortized loan d. none of the above

c. 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: a. an ordinary annuity b. a deferred annuity c. an annuity due d. an extraordinary annuity

c. an annuity due

The method of calculating interest on a loan that is set by law is called the: a. negotiated legal rate (NLR) b. effective annual rate (EAR) c. annual percentage rate (APR) d. none of the above

c. annual percentage rate (APR)

Which of the following terms best describes an annuity due? a. a perpetuity b. unequal payments c. payment at beginning of year d. payment at the end of the year

c. payment at beginning of year

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 contract today, you would need to use: a. present value of a single lump sum b. future value of a single lump sum c. present value of an ordinary annuity d. future value of an ordinary annuity e. present value of an annuity due f. future value of an annuity due

c. present value of an ordinary annuity

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. a. $1,720 b. $1,960 c. $1,200 d. $1,216

d. $1,216 PV 1,000 N 4 I/Y 5 → FV = $1,215.51

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 answer. a. $39,981 b. $46,753 c. $49,002 d. $50,258

d. $50,258

The interest rate that measures the true interest rate when compounding occurs more frequently than once a year is called the: a. annual percentage rate b. compound rate of interest c. stated rate of interest d. effective annual rate

d. effective annual rate

When compounding more than once a year, the true opportunity costs measure of the interest rate is indicated by the: a. annual percentage rate b. contract rate c. stated rate d. effective annual rate

d. effective annual rate