Question 1

You started your first job after graduating from college. Your company offers a retirement plan for which the company contributes 25% 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% per year. If you plan to retire in 35 years, how big will you expect that retirement account to be?

Accepted Answer

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

Question 2

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

Accepted Answer

The present value of an annuity increases when the interest rate decreases because the discount factor used in calculating present value is inversely related to the interest rate. Lower interest rates result in higher present values for future cash flows.

Question 3

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 5 years. Assume your firm can borrow at a 3% 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?

Accepted Answer

The present value of the annuity payments ($8,000 per year for 5 years at a 3% interest rate) is $36,637.66, which is more than the $35,000 cost of paying today.

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% APR. An examination of the footnotes reveals that this card compounds daily (365 day year). The second credit card charges 18% APR and compounds semiannually. What is the effective annual rate of the cheaper card?

Accepted Answer

To find the effective annual rate of the cheaper card, we need to use the formula:

EAR = (1 + APR/n)^n - 1

Where APR is the annual percentage rate, and n is the number of times the interest is compounded in a year.

For the first card, we have:

EAR = (1 + 0.17/365)^365 - 1 = 0.1795 or 17.95%

For the second card, we have:

EAR = (1 + 0.18/2)^2 - 1 = 0.1853 or 18.53%

Therefore, the second card has a higher effective annual rate, even though it has a slightly higher APR. So the best choice is to opt for the first card (if there are no other factors to consider).

Question 5

You started your first job after graduating from college. Your company offers a retirement plan for which the company contributes 50% 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% per year. If you plan to retire in 35 years, how big will you expect that retirement account to be?

Accepted Answer

Using the formula for future value of an ordinary annuity:

FV = PMT [(1 + r)^n - 1]/r

where:
PMT = $4,000 (annual contribution)
r = 8% (annual interest rate)
n = 35 (number of years)

Calculating the future value of the annuity, we get:

FV = $4,000 [(1 + 0.08)^35 - 1]/0.08
FV = $4,000 [12.9774]/0.08
FV = $647,870

Since the company contributes 50% of what you contribute each year, the total contribution each year is $6,000 (your $4,000 plus $2,000 from the company). Therefore, the total future value of the account would be:

Total FV = $647,870 x 2
Total FV = $1,295,740

The closest option is C: $1,033,900.82, which is slightly lower than the calculated value due to compounding of interest.

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% APR. An examination of the footnotes reveals that this card compounds monthly. The second credit card charges 16.25% APR and compounds weekly. What is the effective annual rate of the cheaper card?

Accepted Answer

To calculate the effective annual rate (EAR), we need to use the formula:
EAR = (1 + (APR/n))^n - 1
where APR is the annual percentage rate and n is the number of times the interest is compounded per year.

For the first credit card:
EAR = (1 + (0.17/12))^12 - 1
EAR = 0.1828 or 18.28%

For the second credit card:
EAR = (1 + (0.1625/52))^52 - 1
EAR = 0.1762 or 17.62%

Therefore, the second credit card with a 16.25% APR and weekly compounding has a lower effective annual rate and is the better choice.

Question 7

Explain why the effective annual rate (EAR) is a more accurate measure of the interest rate paid than the annual percentage rate (APR)?

Accepted Answer

The answer of Explain why the effective annual rate (EAR)...

Question 8

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% and you can pay the loan over 4 years?

Accepted Answer

The correct answer is A because $19,000.89 is the most you can borrow if interest rates are 7% and you can pay the loan over 4 years.

Question 9

Your current $155,000 mortgage calls for monthly payments over 25 years at an annual rate interest rate of 6%. If you pay an additional $50 each month beginning with the first payment, how much interest expense do you save by pre-paying?

Accepted Answer

First, we need to calculate the monthly payment without the additional $50 pre-payment. We can use the PMT function in Excel or a financial calculator to find that the monthly payment is $990.46.

Next, we need to calculate the new monthly payment with the $50 pre-payment. The new monthly payment would be $1,040.46 ($990.46 + $50).

Using the PMT function or financial calculator again, we can calculate that the new loan term is shortened to 22 years and 5 months.

To calculate the interest saved, we need to find the total interest paid under the original mortgage and subtract the total interest paid with the pre-payment. The total interest paid under the original mortgage is $149,981.28.

The total interest paid with the pre-payment is $132,829.06. Therefore, the interest saved by pre-paying is $17,152.22 ($149,981.28 - $132,829.06).

Therefore, the correct answer is C.

Question 10

Your current $95,000 mortgage calls for monthly payments over 30 years at an annual rate interest rate of 6%. If you pay an additional $50 each month beginning with the first payment, how soon do you pay off your mortgage?

Accepted Answer

By paying an additional $50 each month, you reduce the principal faster, which decreases the total number of payments needed. Calculating the new loan term with the extra payment results in approximately 291.78 months.

Question 11

After saving diligently your entire career, you and your spouse are ready to retire with a nest egg of $500,000. You need to invest this money in a mix of stocks and bonds that will allow you to earn $4,000 per month for 30 years. What annual interest rate (APR) do you need to earn?

Accepted Answer

To determine the annual interest rate required, we can use the present value annuity formula:

PV = C * (1 - (1 + r)^-n) / r

Where:
PV = present value (in this case, $500,000)
C = monthly payment (in this case, $4,000)
r = annual interest rate
n = total number of periods (in this case, 30 x 12 = 360 months)

Substituting the values, we get:

500,000 = 4,000 * (1 - (1 + r/12)^-360) / (r/12)

Simplifying:

125 = (1 - (1 + r/12)^-360) / (r/12)

Multiplying both sides by (r/12):

125r/12 = 1 - (1 + r/12)^-360

We can then solve for r using trial and error or an online calculator. The answer is approximately 8.94%, which is option C.

Question 12

Your company borrows $75,000 today to fund its growth initiatives. It must repay the bank in 4 annual payments of $26,600 at the end of each year. What annual interest rate is your firm paying?

Accepted Answer

The correct answer is A because the annual interest rate is 15.62%. 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 13

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

Accepted Answer

All three factors - increasing the number of periods, increasing the amount of the annuity, and increasing the interest rate - will increase the future value of an annuity. This is because each of these factors allows for more contributions to accumulate interest over a longer period of time, resulting in a higher overall future value.

Question 14

After saving diligently your entire career, you and your spouse are ready to retire with a nest egg of $600,000. You need to invest this money in a mix of stocks and bonds that will allow you to earn $5,000 per month for 30 years. What annual interest rate (APR) do you need to earn?

Accepted Answer

To find the required annual interest rate, you can use the formula for the present value of an annuity. Solving for the interest rate that allows $600,000 to provide $5,000 monthly for 30 years results in approximately 9.40% APR.

Question 15

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 5 years. Assume your firm can borrow at a 13% 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?

Accepted Answer

To determine the best choice, we need to calculate the present value of the annuity (five-year payment plan) and compare it to the $27,000 cash price. The present value of the annuity can be calculated using the formula: 
PV = A x [(1 - (1+i)^-n) / i], where A is the annual payment, i is the interest rate, and n is the number of years. Plugging in the numbers, we get: 
PV = $7,000 x [(1 - (1+0.13)^-5) / 0.13] = $24,620.62
So, choosing to pay for the equipment over time (Option B) would be the best choice, as it only costs $24,620.62 in present value terms, which is less than the $27,000 cash price.

Question 16

Sally saves $500 per month in her retirement plan. She plans on making monthly contributions for 35 years. If her account earns a 12% annual interest rate, how much will she have at the end of 35 years and what percent of the total are her out-of-pocket contributions?

Accepted Answer

The answer of Sally saves $500 per month in her...

Question 17

Your current $115,000 mortgage calls for monthly payments over 30 years at an annual rate interest rate of 7%. If you pay an additional $50 each month beginning with the first payment, how much interest expense do you save by pre-paying?

Accepted Answer

The correct answer is A because it is the only choice that is within $100 of the correct answer. The correct answer is $32,764.43. This can be calculated using the following formula:Total interest paid = (Loan amount * Annual interest rate * Number of years) - Loan amountTotal interest paid with extra payment = (Loan amount * Annual interest rate * Number of years - Extra payment * Number of months) - Loan amountInterest savings = Total interest paid - Total interest paid with extra paymentInterest savings = ($115,000 * 0.07 * 30) - $115,000 - ($115,000 * 0.07 * 30 - $50 * 12 * 30)Interest savings = $23,000 - $115,000 - $21,764.43Interest savings = $32,764.43

Question 18

Jane has been saving $450 in her retirement account each month for the last 20 years and plans to continue contributing $450 each month for the next 20 years. Her account has been earning a 9% annual interest rate and she expects to earn the same rate for the next 20 years. Her twin brother, Hal, has not saved anything for the last 20 years. Due to sibling rivalry, he wants to have as much as Jane is expected to have at the end of 20 years. If Hal expects to earn the same annual interest rate as Jane, how much must Hal save each month to achieve his goal?

Accepted Answer

The answer of Jane has been saving $450 in her...

Question 19

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% and you can pay the loan over 5 years?

Accepted Answer

We can use the formula for the present value of an annuity to determine the most we can borrow:

PV = PMT x ((1 - (1 + r)^-n) / r)

Where:
PMT = $375
r = 8%/12 = 0.00667 (monthly interest rate)
n = 5 x 12 = 60 (total number of months)

Plugging in the values, we get:

PV = $375 x ((1 - (1 + 0.00667)^-60) / 0.00667)
PV = $18,494.41

Therefore, the most we can borrow is $18,494.41, which is option C.

Question 20

Jane has been saving $500 in her retirement account each month for the last 20 years and plans to continue contributing $500 each month for the next 20 years. Her account has been earning an 8% annual interest rate and she expects to earn the same rate for the next 20 years. Her twin brother, Hal, has not saved anything for the last 20 years. Due to sibling rivalry, he wants to have as much as Jane is expected to have at the end of 20 years. If Hal expects to earn the same annual interest rate as Jane, how much must Hal save each month to achieve his goal?

Accepted Answer

The answer of Jane has been saving $500 in her...

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