Question 1

Which of the following statements is correct?
A) A 15-year mortgage will have larger monthly payments than a 30-year mortgage.
B) If an account earns 3 percent per year compounded annually, then it also has an effective annual rate (EAR) of 3 percent.
C) The present value of a $500 perpetuity is greater if the interest rate is higher.
D) The first, second, and third statements above are correct.
E) Only the first and second, statements above are correct.

Accepted Answer

The answer of Which of the following statements is correct?
A)...

Question 2

Your company borrows $275,000 today to fund its growth initiatives. It must repay the bank in five annual payments of $76,300 at the end of each year. What annual interest rate is your firm paying?
A) 10.85 percent
B) 12.01 percent
C) 17.75 percent
D) 18.02 percent

Accepted Answer

The annual interest rate can be found using the formula for the present value of an annuity. Solving for the interest rate that equates the present value of the annuity payments ($76,300 for 5 years) to the loan amount ($275,000) gives approximately 12.01 percent.

Question 3

Which of the following will decrease the present value of an annuity?
A) The discount rate increases.
B) The discount rate decreases.
C) The number of periods the annuity is received increases.
D) The final payment increases.

Accepted Answer

An increase in the discount rate decreases the present value of an annuity because future cash flows are discounted at a higher rate, making them worth less in today's dollars.

Question 4

As a college student, you probably receive many credit card offers in the mail. Consider these two offers. The first card charges a 17 percent APR. An examination of the footnotes reveals that this card compounds monthly. The second credit card charges 16.25 percent APR and compounds weekly. What is the effective annual rate of the cheaper card?
A) 17.00 percent
B) 17.62 percent
C) 16.25 percent
D) 18.39 percent

Accepted Answer

The effective annual rate (EAR) can be calculated using the formula EAR = (1 + i/n)^(n*12) - 1, where i is the annual interest rate and n is the number of compounding periods per year. For the first card with a 17% APR compounded monthly, EAR = (1 + 0.17/12)^(12) - 1 = 17.62%. For the second card with a 16.25% APR compounded weekly, EAR = (1 + 0.1625/52)^(52) - 1, which is less than 17.62% but not one of the options provided. Therefore, the correct answer is the EAR of the first card, which is 17.62%.

Question 5

You have reviewed your budget and determine that the most you can afford on a car loan is $455 per month. What is the most you can borrow if interest rates are 7 percent and you can pay the loan over four years?
A) $19,000.89
B) $19,741.29
C) $20,074.82
D) $21,671.53

Accepted Answer

The correct answer is A because $19,000.89 is the most you can borrow if interest rates are 7 percent and you can pay the loan over four years.

Question 6

As a college student, you probably receive many credit card offers in the mail. Consider these two offers. The first card charges a 17 percent APR. An examination of the footnotes reveals that this card compounds daily (365 day year). The second credit card charges 18 percent APR and compounds semiannually. What is the effective annual rate of the cheaper card?
A) 18.00 percent
B) 17.00 percent
C) 18.81 percent
D) 18.53 percent

Accepted Answer

The effective annual rate (EAR) for the first card is calculated using the formula: EAR = (1 + APR/n)^n - 1, where n is the number of compounding periods per year. For daily compounding, n = 365. Thus, EAR = (1 + 0.17/365)^365 - 1 ≈ 18.53%.

Question 7

Which of the following will increase the present value of an annuity?
A) The discount rate increases.
B) The discount rate decreases.
C) The number of periods the annuity is received decreases.
D) The final payment diminishes.

Accepted Answer

The present value of an annuity increases when the discount rate decreases because future cash flows are discounted at a lower rate, making their present value higher.

Question 8

You started your first job after graduating from college. Your company offers a retirement plan for which the company contributes 50 percent of what you contribute each year. You expect to contribute $4,000 per year from your salary. You decide to invest the contributions in assets that you expect to earn 8 percent per year. If you plan to retire in 35 years, how big will you expect that retirement account to be?
A) $689,267.21
B) $823,147.29
C) $1,033,900.82
D) $1,308,427.41

Accepted Answer

The correct answer is found by calculating the future value of the annual contributions using the formula for the future value of an annuity. Since the company matches 50% of the $4,000 contribution, the total annual contribution is $6,000. Using an 8% annual return over 35 years, the future value can be calculated, which matches closest to option C, $1,033,900.82.

Question 9

Bank A charges a 7.75 percent annual percentage rate and interest is due at the end of the year. Bank B charges a 7 percent annual percentage rate and interest must be paid monthly. What is the effective annual rate charged by each bank?
A) Bank A: 7.75 percent, Bank B: 7.23 percent
B) Bank A: 7.85 percent, Bank B: 7.23 percent
C) Bank A: 7.25 percent, Bank B: 7.5 percent
D) Bank A: 7.85 percent, Bank B: 8.15 percent

Accepted Answer

Bank A's effective annual rate is exactly its stated annual percentage rate of 7.75 percent since interest is compounded annually. Bank B's effective annual rate is higher than its stated rate due to monthly compounding. The effective annual rate for Bank B can be calculated using the formula for effective annual rate (EAR) = (1 + r/n)^(n*p) - 1, where r is the annual interest rate, n is the number of compounding periods per year, and p is the number of years. Plugging in Bank B's values: EAR = (1 + 0.07/12)^(12*1) - 1 ≈ 7.23 percent.

Question 10

You have reviewed your budget and determine that the most you can afford on a car loan is $375 per month. What is the most you can borrow if interest rates are 8 percent and you can pay the loan over five years?
A) $20,591.86
B) $16,779.02
C) $18,494.41
D) $21,147.83

Accepted Answer

The answer of You have reviewed your budget and determine...

Question 11

Your company borrows $75,000 today to fund its growth initiatives. It must repay the bank in four annual payments of $26,600 at the end of each year. What annual interest rate is your firm paying?
A) 15.62 percent
B) 17.18 percent
C) 14.74 percent
D) 16.97 percent

Accepted Answer

The correct answer is A because the annual interest rate is 15.62 percent. This can be calculated using the formula for the present value of an annuity, which is:PV = PMT * [1 - (1 + r)^-n] / rwhere:PV is the present value of the annuityPMT is the annual paymentr is the annual interest raten is the number of yearsIn this case, we have:PV = $75,000PMT = $26,600n = 4Substituting these values into the formula, we get:$75,000 = $26,600 * [1 - (1 + r)^-4] / rSolving for r, we get:r = 15.62%

Question 12

You are deciding among several different bank accounts. Which of the following will generate the highest effective annual rate (EAR)?
A) a 6 percent rate with monthly compounding
B) a 6 percent rate with annual compounding
C) a 6.08 percent rate with annual compounding
D) a 6 percent rate with quarterly compounding

Accepted Answer

Monthly compounding generates the highest EAR because the interest is compounded more frequently.

Question 13

Your company borrows $55,000 today to fund its growth initiatives. It must repay the bank in four annual payments of $17,100 at the end of each year. What annual interest rate is your firm paying?
A) 7.76 percent
B) 8.26 percent
C) 9.33 percent
D) 10.26 percent

Accepted Answer

The annual interest rate can be calculated using the formula for the present value of an annuity. Solving for the interest rate that equates the present value of the annuity payments ($17,100 for 4 years) to the loan amount ($55,000) results in an interest rate of approximately 9.33 percent.

Question 14

You are deciding among several different bank accounts. Which of the following will generate the highest effective annual rate (EAR)?
A) a 10 percent rate with monthly compounding
B) a 10 percent rate with annual compounding
C) a 10.5 percent rate with annual compounding
D) a 10 percent rate with quarterly compounding

Accepted Answer

The effective annual rate (EAR) takes into account the impact of compounding within a year. A higher nominal interest rate with the same compounding frequency will always result in a higher EAR. Therefore, a 10.5 percent rate with annual compounding (C) will generate the highest EAR compared to a 10 percent rate with any compounding frequency.

Question 15

You just bought a new home and have a 30-year mortgage with monthly payments. Which statement regarding your mortgage is correct?
A) Your monthly payments will decrease over time.
B) The dollar amount of interest expense you pay each year will remain the same each year.
C) The dollar amount of principal paid increases each month.
D) All of these choices are correct.

Accepted Answer

In a typical mortgage structure, the total monthly payment remains the same throughout the term, but the composition of the payment changes over time. Early in the term, a larger portion of each payment is applied toward interest. As the principal balance decreases, the interest expense decreases, and the portion of the payment applied to the principal increases. Therefore, the dollar amount of principal paid increases with each payment.

Question 16

Bank A charges a 7.50 percent annual percentage rate and interest is due at the end of the year. Bank B charges a 6.95 percent annual percentage rate and interest must be paid monthly. What is the effective annual rate charged by each bank?
A) Bank A: 7.5 percent, Bank B: 6.95 percent
B) Bank A: 7.76 percent, Bank B: 6.95 percent
C) Bank A: 7.5 percent, Bank B: 7.18 percent
D) Bank A: 7.76 percent, Bank B: 7.18 percent

Accepted Answer

Bank A's effective annual rate (EAR) is exactly its annual percentage rate (APR) of 7.5% since interest is compounded annually. For Bank B, the APR is 6.95%, but since interest is compounded monthly, the EAR is higher. The formula to calculate EAR for monthly compounding is $(1 + \frac{APR}{n})^n - 1$, where $n$ is the number of compounding periods per year (12 for monthly). Plugging Bank B's APR into this formula gives an EAR greater than 6.95%, specifically around 7.18%.

Question 17

Your firm needs to buy additional physical therapy equipment that costs $35,000. The equipment manufacturer will give you the equipment now if you will pay $8,000 per year for the next five years. Assume your firm can borrow at a 3 percent interest rate. You need to analyze if your firm should pay the manufacturer the $35,000 now or accept the five-year annuity offer of $8,000. Which of the following statements is correct?
A) You decide to pay $35,000 today because paying in cash is always cheaper.
B) You decide to pay $35,000 today because paying for the equipment over time costs $36,637.66.
C) You decide to pay for the equipment over time because it only costs $39,112.86.
D) Paying for the equipment over time costs $36,637.66, which is less than paying $35,000 today.

Accepted Answer

To determine the correct choice, you calculate the present value of the annuity (the series of $8,000 payments) using the given interest rate of 3%. The calculation shows that the total cost of paying over time is $36,637.66, which is more expensive than paying $35,000 upfront. Therefore, it's financially wiser to pay the $35,000 today.

Question 18

You have reviewed your budget and determine that the most you can afford on a car loan is $550 per month. What is the most you can borrow if interest rates are 6 percent and you can pay the loan over three years?
A) $1,470.16
B) $15,639.28
C) $17,641.92
D) $18,079.06

Accepted Answer

The answer of You have reviewed your budget and determine...

Question 19

Your firm needs to buy additional physical therapy equipment that costs $27,000. The equipment manufacturer will give you the equipment now if you will pay $7,000 per year for the next five years. Assume your firm can borrow at a 13 percent interest rate. You need to analyze if your firm should pay the manufacturer the $27,000 now or accept the five-year annuity offer of $7,000. Which of the following statements is correct?
A) You decide to pay $27,000 today because paying in cash is always cheaper.
B) You decide to pay for the equipment over time because it only costs $24,620.62.
C) You decide to pay for the equipment over time because it only costs $29,112.86.
D) You decide to pay $27,000 today because it is cheaper than paying for the equipment over time.

Accepted Answer

The answer of Your firm needs to buy additional physical...

Question 20

You started your first job after graduating from college. Your company offers a retirement plan for which the company contributes 25 percent of what you contribute each year. You expect to contribute $5,000 per year from your salary. You decide to invest the contributions in assets that you expect to earn 8 percent per year. If you plan to retire in 35 years, how big will you expect that retirement account to be?
A) $861,584.02
B) $921,597.31
C) $972,110.74
D) $1,076,980.02

Accepted Answer

The answer of You started your first job after graduating...

Quiz 5: Time Value of Money 2: Analyzing Annuity Cash Flows

Which of the following statements is correct?

Your company borrows $275,000 today to fund its growth initiatives. It must repay the bank in five annual payments of $76,300 at the end of each year. What annual interest rate is your firm paying?

Which of the following will decrease the present value of an annuity?

You have reviewed your budget and determine that the most you can afford on a car loan is $455 per month. What is the most you can borrow if interest rates are 7 percent and you can pay the loan over four years?

Which of the following will increase the present value of an annuity?

Bank A charges a 7.75 percent annual percentage rate and interest is due at the end of the year. Bank B charges a 7 percent annual percentage rate and interest must be paid monthly. What is the effective annual rate charged by each bank?

You have reviewed your budget and determine that the most you can afford on a car loan is $375 per month. What is the most you can borrow if interest rates are 8 percent and you can pay the loan over five years?

Your company borrows $75,000 today to fund its growth initiatives. It must repay the bank in four annual payments of $26,600 at the end of each year. What annual interest rate is your firm paying?

You are deciding among several different bank accounts. Which of the following will generate the highest effective annual rate (EAR) ?

Your company borrows $55,000 today to fund its growth initiatives. It must repay the bank in four annual payments of $17,100 at the end of each year. What annual interest rate is your firm paying?

You are deciding among several different bank accounts. Which of the following will generate the highest effective annual rate (EAR) ?

You just bought a new home and have a 30-year mortgage with monthly payments. Which statement regarding your mortgage is correct?

Bank A charges a 7.50 percent annual percentage rate and interest is due at the end of the year. Bank B charges a 6.95 percent annual percentage rate and interest must be paid monthly. What is the effective annual rate charged by each bank?

You have reviewed your budget and determine that the most you can afford on a car loan is $550 per month. What is the most you can borrow if interest rates are 6 percent and you can pay the loan over three years?