Deck 4: Future Value, Present Value and Interest Rates

Question 1

Suppose a family wants to save $60,000 for a child's tuition. The child will be attending college in 18 years. For simplicity, assume the family is saving for a one-time college tuition payment. If the interest rate is 6%, then about how much does this family need to deposit in the bank today?

A) $10,000
B) $21,000
C) $42,000
D) $57,000

Answer 1

B

Question 2

Compound interest means that:

A) you get an interest deduction for paying your loan off early.
B) you get interest on interest.
C) you get an interest deduction if you take out a loan for longer than one year.
D) interest rates will rise on larger loans.

Answer 2

B

Question 3

Which of the following best expresses the proceeds a lender receives from a one-year simple loan when the annual interest rate equals i?

A) PV + i
B) FV/i
C) PV(1 + i)
D) PV/i

Answer 3

C

Question 4

A promise of a $100 payment to be received one year from today is:

A) more valuable than receiving the payment today.
B) less valuable than receiving the payment two years from now.
C) equally valuable as a payment received today if the interest rate is zero.
D) not enough information is provided to answer the question.

Question 5

Suppose Mary receives an $8,000 loan from First National Bank. Mary repays $8,480 to First National Bank at the end of one year. Assuming the simple calculation of interest, the interest rate on Mary's loan was:

A) 8.00%
B) $480
C) 6.00%
D) 5.66%

Question 6

Which of the following expresses 4.85%?

A) 0.0485
B) 4.850
C) 0.00485
D) 0.485

Question 7

Suppose that Stephen Curry, a basketball player for the Golden State Warriors, will become a free agent at the end of this NBA season. Suppose that Curry is considering two possible contracts from different teams. Note that the salaries are paid at the end of EACH year.
The interest rate is 10%. Based on this information, which of the following is true?

A) Curry should take the Boston contract because it has a higher present value.
B) Curry should take the Portland contract because it has a higher present value.
C) Curry is indifferent between the two contracts because they are both worth $12 million.
D) Curry is indifferent between the two contracts because they are both worth $10.9 million.

Question 8

An investor deposits $400 into a bank account that earns an annual interest rate of 8%. Based on this information, how much interest will he earn during the second year alone?

A) $25.60
B) $32
C) $34.56
D) $64

Question 9

If a saver has a positive rate of time preference then the present value of $100 to be received 1 year from today is:

A) more than $100.
B) not calculable.
C) less than 100.
D) unknown to the saver.

Question 10

Suppose Paul borrows $4,000 for one year from his grandfather who charges Paul 7% interest. At the end of the year Paul will have to repay his grandfather:

A) $4,280
B) $4,290
C) $4,350
D) $4,820

Question 11

A lender is promised a $100 payment (including interest) one year from today. If the lender has a 6% opportunity cost of money, he/she should be willing to accept what amount today?

A) $100.00
B) $106.20
C) $96.40
D) $94.34

Question 12

The future value of $100 at a 5% per year interest rate at the end of one year is:

A) $95.00
B) $105.00
C) $97.50
D) 107.50

Question 13

Which of the following expresses 5.5%?

A) 0.0055
B) 5.50
C) 0.550
D) 0.0550

Question 14

Which of the following best expresses the payment a saver receives for investing their money for two years?

A) PV + PV
B) PV + PV (1 + i)
C) PV(1 + i)²
D) 2PV(1 + i)

Question 15

Suppose Tom receives a one-year loan from ABC Bank for $5,000.00. At the end of the year, Tom repays $5,400.00 to ABC Bank. Assuming the simple calculation of interest, the interest rate on Tom's loan was:

A) $400
B) 8.00%
C) 7.41%
D) 20%

Question 16

Credit:

A) probably came into being at the same time as coinage.
B) predates coinage by 2,000 years.
C) did not exist until the middle ages.
D) first became popular due to the writings of Aristotle.

Question 17

Which of the following expresses 5.65%?

A) 0.565
B) 0.00565
C) 5.65
D) 0.0565

Question 18

Which of the following best expresses the payment a lender receives for lending money for three years?

A) 3PV
B) PV/(1+i)³
C) PV/(1 + i)³
D) FV/ (1 + i)³

Question 19

Farou invests $2,000 at 8% interest. About how long will it take for Farou to double his investment (e.g., to have $4,000)?

A) 4 years
B) 5 years
C) 8 years
D) 9 years

Question 20

If the interest rate is zero, a promise to receive a $100 payment one year from now is:

A) more valuable than receiving $100 today.
B) less valuable than receiving $100 today.
C) equal in value to receiving $100 today.
D) equal in value to receiving $101 today.

Question 21

In reading the national business news, you hear that mortgage rates increased by 50 basis points. If mortgage rates were initially at 6.5%, what are they after this increase?

A) 6.55%
B) 7.0%
C) 11.5%
D) 56.5%

Question 22

The future value of $200 that is left in account earning 6.5% interest for three years is best expressed by which of the following?

A) $200(1.065) × 3
B) $200(1.065)/3
C) $200(1.065)ⁿ
D) $200(1.065)³

Question 23

What is the future value of $1,000 after six months earning 12% annually?

A) $1,050.00
B) $1,060.00
C) $1,120.00
D) $1,058.30

Question 24

Which of the following best expresses the future value of $100 left in a savings account earning 3.5% for three and a half years?

A) $100(1.035)³.⁵
B) $100(0.35)³.⁵
C) $100 × 3.5 × (1.035)
D) $100(1.035)³/2

Question 25

Sharon deposits $150.00 in her savings account at the bank. At the end of one year she has $156.38. What was the interest rate that Sharon earned?

A) 4.25%
B) 6.38%
C) 4.52%
D) 5.63%

Question 26

A saver knows that if she put $95 in the bank today she will receive $100 from the bank one year from now, including the interest she will earn. What is the interest rate she is earning?

A) 5.10%
B) 6.00%
C) 5.52%
D) 5.26%

Question 27

Tom deposits funds in his savings account at the bank which is paying 3.5% interest. If he keeps his funds in the bank for one year he will have $155.25. What amount is Tom depositing?

A) $151.75
B) $150.00
C) $148.75
D) $147.50

Question 28

Mary deposits funds into a CD at her bank. The CD has an annual interest of 4.0%. If Mary leaves the funds in the CD for two years she will have $540.80. Assuming no penalties for withdrawing the funds early, what amount would Mary have at the end of one year?

A) $521.60
B) $490.00
C) $500.00
D) $520.00

Question 29

One hundred basis points could be expressed as:

A) 0.01%
B) 1.00%
C) 100.0%
D) 0.10%

Question 30

What is the present value of $200 promised two years from now at 5% annual interest?

A) $190.00
B) $220.00
C) $180.00
D) $181.41

Question 31

The value of $100 left in a certificate of deposit for four years that earns 4.5% annually will be:

A) $120.00
B) $119.25
C) $117.00
D) $145.00

Question 32

The rule of 72 says that at 6% interest $100 should become $200 in about:

A) 72 months
B) 100 months
C) 12 years
D) 7.2 years

Question 33

According to the rule of 72:

A) any amount should double in value in 72 months if invested at 10%.
B) 72/interest rate is the number of years approximately it will take for an amount to double.
C) 72 × interest rate is the number of years it will take for an amount to double.
D) the interest rate divided by the number of years invested will always equal 72%.

Question 34

The future value of $100 that earns 10% annually for n years is best expressed by which of the following?

A) $100(0.1)ⁿ
B) $100 × n × (1.1)
C) $100(1.1)ⁿ
D) $100/(1.1)ⁿ

Question 35

What is the present value of $100 promised one year from now at 10% annual interest?

A) $89.50
B) $90.00
C) $90.91
D) $91.25

Question 36

Mary deposits funds into a CD at her bank. The CD has an annual interest of 4.0%. If Mary leaves the funds in the CD for two years she will have $540.80. What amount is Mary depositing?

A) $520.00
B) $514.50
C) $500.00
D) $512.40

Question 37

The value of $100 left in a savings account earning 5% a year, will be worth what amount after ten years?

A) $150.00
B) $160.50
C) $159.84
D) $162.89

Question 38

The decimal equivalent of a basis point is:

A) 0.0001
B) 1.00
C) 0.001
D) 0.01

Question 39

Which of the following best expresses the present value of $500 that you have to wait four years and three months to receive?

A) ($500/4.25) × (1 + i)
B) $500 × 4.25 × (1 + i)
C) $500/(1 + i)⁴.²⁵
D) ($500/4) × (1 + i)³

Question 40

If 10% is the annual rate, considering compounding, the monthly rate is:

A) 0.0833%
B) 0.833%
C) 0.80%
D) 1.0833%

Question 41

Doubling the future value will cause:

A) the present value to fall by half.
B) the interest rate, i, to double.
C) no change to present value, only the interest rate.
D) the present value to double.

Question 42

The present value and the interest rate have:

A) a direct relationship; as i increases, pv increases.
B) an inverse relationship; as i increases, pv decreases.
C) an unclear relationship; whether it is direct or inverse depends on the interest rate.
D) no relationship.

Question 43

Doubling the future value will cause the:

A) present value to double.
B) present value to decrease.
C) present value to increase by less than 100%.
D) interest rate, i, to decrease.

Question 44

A mortgage, where the monthly payments are the same for the duration of the loan, is an example of a(n):

A) variable payment loan.
B) installment loan.
C) fixed payment loan.
D) equity security.

Question 45

If the internal rate of return from an investment is more than the opportunity cost of funds the firm should:

A) make the investment.
B) not make the investment.
C) only make the investment using retained earnings.
D) only make part of the investment and wait to see if interest rates decrease.

Question 46

The "coupon rate" is:

A) the annual amount of interest payments made on a bond as a percentage of the amount borrowed.
B) the change in the value of a bond expressed as a percentage of the amount borrowed.
C) another name for the yield on a bond, assuming the bond is sold before it matures.
D) the total amount of interest payments made on a bond as a percentage of the amount borrowed.

Question 47

An investment has grown from $100.00 to $130.00 or by 30% over four years. What annual increase gives a 30% increase over four years?

A) 7.50%
B) 6.30%
C) 6.78%
D) 7.24%

Question 48

An investment carrying a current cost of $120,000 is going to generate $50,000 of revenue for each of the next three years. To calculate the internal rate of return we need to:

A) calculate the present value of each of the $50,000 payments and multiply these and set this equal to $120,000.
B) find the interest rate at which the present value of $150,000 for three years from now equals $120,000.
C) find the interest rate at which the sum of the present values of $50,000 for each of the next three years equals $120,000.
D) subtract $120,000 from $150,000 and set this difference equal to the interest rate.

Question 49

A monthly growth rate of 0.6% is an annual growth rate of:

A) 7.20%
B) 6.00%
C) 7.60%
D) 7.44%

Question 50

A change in the interest rate:

A) has a smaller impact on the present value of a payment to be made far into the future than on one to be made sooner.
B) will not make a difference in the present values of two equal payments to be made at different times.
C) has a larger impact on the present value of a payment to be made far into the future than on one to be made sooner.
D) has a larger impact on the present value of a bigger payment to be made far into the future than on one of lesser value.

Question 51

The internal rate of return of an investment is:

A) the same as return on investment.
B) zero when the present value of an investment equals its cost.
C) the interest rate that equates the present value of an investment with its cost.
D) equal to the market rate of interest when an investment is made.

Question 52

The shorter the time until a payment the:

A) higher the present value.
B) lower the present value because time is valuable.
C) lower must be the interest rate.
D) higher must be the interest rate.

Question 53

At any fixed interest rate, an increase in time, n, until a payment is made:

A) increases the present value.
B) has no impact on the present value since the interest rate is fixed.
C) reduces the present value.
D) affects only the future value.

Question 54

An investment grows from $100.00 to $150.00 or 50% over five years. What annual increase gives a 50% increase over five years?

A) 12.00%
B) 10.00%
C) 9.25%
D) 8.45%

Question 55

A monthly growth rate of 0.5% is an annual growth rate of:

A) 6.00%
B) 5.00%
C) 6.17%
D) 6.50%

Question 56

What is the present value of $500 promised four years from now at 5% annual interest?

A) $411.35
B) $400.00
C) $607.75
D) $520.00

Question 57

Higher savings usually requires higher interest rates because:

A) everyone prefers to save more instead of consuming.
B) saving requires sacrifice and people must be compensated for this sacrifice.
C) higher savings means we expect interest rates to decrease.
D) of the rule of 72.

Question 58

The lower the interest rate, i, the:

A) lower is the present value.
B) greater must be n.
C) higher is the present value.
D) higher is the future value.

Question 59

The higher the future value of the payment the:

A) lower the present value.
B) higher the present value.
C) future value doesn't impact the present value, only the interest rate really matters.
D) lower the present value because the interest rate must fall.

Question 60

A monthly interest rate of 1% is a compounded annual rate of :

A) 12.68%
B) 10.00%
C) 14.11%
D) 6.00%

Question 61

The price of a coupon bond is determined by taking the present value of:

A) the bond's final payment and subtracting the coupon payments.
B) the coupon payments and adding this to the face value.
C) the bond's final payment.
D) all of the bond's payments.

Question 62

The price of a coupon bond is determined by:

A) taking the present value of the bond's final payment and subtracting the coupon payments.
B) taking the present value of the coupon payments and adding this to the face value.
C) taking the present value of all of the bond's payments.
D) estimating its future value.

Question 63

Which formula below best expresses the real interest rate, (r)?

A) i = r - e
B) r = i + e
C) r = i - e
D) e = i + r

Question 64

A coupon bond is a bond that:

A) always sells at a price that is less than the face value.
B) provides the owner with regular payments.
C) pays the owner the sum of the coupons at the bond's maturity.
D) pays a variable coupon rate depending on the bond's price.

Question 65

A credit card that charges a monthly interest rate of 1.5% has an effective annual interest rate of:

A) 18.0%
B) 19.6%
C) 15.0%
D) 17.50%

Question 66

Suppose the nominal interest rate on a one-year car loan is 8% and the inflation rate is expected to be 3% over the next year. Based on this information, we know:

A) the ex ante real interest rate is 5%.
B) the lender benefits more than the borrower because of the difference in the nominal versus real interest rates.
C) at the end of the year, the borrower pays only 5% in nominal interest.
D) the ex post real interest rate 11%.

Question 67

If a bond has a face value of $1,000 and the bondholder receives coupon payments of $27.50 semi-annually, the bond's coupon rate is:

A) 2.75%
B) 5.50%
C) 27.5%
D) a value that cannot be determined from the information provided.

Question 68

If a bond has a face value of $1,000 and a coupon rate of 4.25%, the bond owner will receive annual coupon payments of:

A) $425.00
B) $4.25
C) $42.50
D) a value that cannot be determined from the information provided.

Question 69

Compounding refers to the

A) calculation of after tax interest returns.
B) internal rate of return a firm earns on an investment.
C) real interest return after taxes.
D) process of earning interest on both the principal and the interest of an investment.

Question 70

Which of the following is necessarily true of coupon bonds?

A) The price exceeds the face value.
B) The coupon rate exceeds the interest rate.
C) The price is equal to the coupon payments.
D) The price is the sum of the present value of coupon payments and the face value.

Question 71

Considering the data on real and nominal interest rates for the U.S. from 1979 to 2012, which of the following statements is most accurate?

A) The real interest rate remains unchanged over time.
B) There have been times when the real interest rate has been negative.
C) Nominal interest rates higher in 2000 than they had been at any other point in time.
D) The inflation rate is always greater than the real interest rate.

Question 72

Usually an investment will be profitable if:

A) the internal rate of return is less than the cost of borrowing.
B) the cost of borrowing is equal to the internal rate of return.
C) it is financed with retained earnings.
D) the cost of borrowing is less than the internal rate of return.

Question 73

Which of the following statements is most correct?

A) We can always compute the ex post real interest rate but not the ex ante real rate.
B) We cannot compute either the ex post or ex ante real interest rates accurately.
C) We can accurately compute the ex ante real interest rate but not the ex post real rate.
D) None of the statements are correct.

Question 74

The price of a coupon bond will increase as the:

A) face value decreases.
B) yield increases.
C) coupon payments increase.
D) term to maturity is shorter.

Question 75

The coupon rate for a coupon bond is equal to the:

A) annual coupon payment divided by the face value of the bond.
B) annual coupon payment divided by the purchase price of the bond.
C) purchase price of the bond divided by the coupon payment.
D) annual coupon payment divided by the selling price of the bond.

Question 76

As inflation increases, for any fixed nominal interest rate, the real interest rate:

A) also increases.
B) remains the same, that's why it is real.
C) decreases.
D) decreases by less than the increase in inflation.

Question 77

Consider a bond that costs $1,000 today and promises a one-time future payment of $1,080 in four years. What is the approximate interest rate on this bond?

A) 2%
B) 4%
C) 8%
D) 10.8%

Question 78

A borrower who makes a $1,000 loan for one year and earns interest in the amount of $75, earns what nominal interest rate and what real interest rate if inflation is two percent?

A) A nominal rate of 5.5% and a real rate of 2.0%.
B) A nominal rate of 7.5% and a real rate of 5.0%.
C) A nominal rate of 7.5% and a real rate of 9.5%.
D) A nominal rate of 7.5% and a real rate of 5.5%.

Question 79

The interest rate that equates the price of a bond with the present value of its payments:

A) will vary directly with the value of the bond.
B) should be the one that makes the value equal to the par value of the bond.
C) will vary inversely with the value of the bond.
D) should always be greater than the coupon rate.

Question 80

Interest rates that are adjusted for expected inflation are known as:

A) coupon rates.
B) ex ante real interest rates.
C) ex post real interest rates.
D) nominal interest rates.