Question 1

Assume a five-year equal payment amortization schedule with an annual interest rate of 12% and annual payments. If the beginning principal is $8,000, then the first interest payment will be how large?
A) $960.00
B) $1,200.00
C) $2,219.28
D) There is not enough information to answer this question.

Accepted Answer

The annual interest rate is 12%, so the periodic interest rate is 1% (12%/12 months). The annual payment is equal to the present value of an annuity factor of 5 years at 12%, which is $2,333.88. The monthly payment is $2,333.88/12, which is $194.49.

To calculate the first interest payment, we need to find the interest on the beginning principal of $8,000 for the first month. The interest is calculated by multiplying the beginning principal by the periodic interest rate.

Interest for the first month = $8,000 x 1% = $80

Therefore, the first interest payment is $80. Answer choice A is correct.

Question 2

Amortization tables are common and can be used for all but which of the following?
A) Car loans
B) Mortgage loans
C) Consumer product loans
D) Amortization tables may be used for all of the above.

Accepted Answer

Amortization tables can be used to calculate the repayment schedule and interest charges for all types of loans, including car loans, mortgage loans, and consumer product loans. Therefore, option D is the correct choice.

Question 3

Your parents have an investment portfolio of $400,000, and they wish to take out cash flows of $50,000 per year as an ordinary annuity. How long will their portfolio last if the portfolio is invested at an annual rate of 4.50%? Use a calculator to determine your answer.
A) 8.00 years
B) 9.10 years
C) 9.60 years
D) 10.14 years

Accepted Answer

Using the formula for present value of an ordinary annuity, we have:
PV = C[(1 - (1 + r)^-n)/r]
where PV is the present value of the cash flows, C is the cash flow per year, r is the annual interest rate, and n is the number of years.

Rearranging the formula to solve for n, we have:
n = -log(1 - (PV*r/C))/log(1 + r)

Plugging in the values given:
PV = 400,000
C = 50,000
r = 0.045
n = -log(1 - (400,000*0.045/50,000))/log(1 + 0.045) = 10.14 years

Therefore, the portfolio will last for 10.14 years if your parents take out cash flows of $50,000 per year as an ordinary annuity invested at an annual rate of 4.50%. The best choice is D.

Question 4

Edward wishes to save enough money to purchase a retirement lake cabin. He is willing to spend $500,000 for the cabin and he can save $25,000 per year and invest the money into an account earning 8.00% per year. If Edward's investments come in the form of equal annual end-of-the-year cash flows and the first cash flow is in exactly one year, how long will it take him to save enough money to buy the lake cabin?
A) Between 8 and 9 years
B) Between 10 and 11 years
C) Between 12 and 13 years
D) Exactly 20 years

Accepted Answer

The answer of Edward wishes to save enough money to...

Question 5

You have a choice among three types of loan and wish to pay the LEAST total cash flows. An amortized loan will result in fewer dollars paid out than a discount or an interest-only loan for the same amount, positive interest rate, and time period.

Accepted Answer

An amortized loan includes both principal and interest payments, spread out over the life of the loan. This means that each payment goes towards paying off both the principal and interest, so the total amount paid in cash flows will be smaller compared to a discount or interest-only loan, which may require a lump sum payment or higher overall interest payments, respectively.

Question 6

Once you begin making payments on an amortization schedule for a loan such as a mortgage or car loan, most contracts clearly state that you may NOT pay off the loan early.

Accepted Answer

Most contracts allow for early payoff of loans, although some may include prepayment penalties. It is important to review the terms of a loan agreement before signing.

Question 7

Amortization tables are useful for each of the following reasons EXCEPT:
A) determining the principal balance due if the loan is being paid off early.
B) determining how much of a total payment is interest and how much is principal for tax purposes.
C) determining the regular periodic total payment.
D) All of these are useful purposes of an amortization table.

Accepted Answer

All three options listed are useful purposes of an amortization table.

Question 8

Marie has a $1,000,000 investment portfolio and she wishes to spend $87,500 per year as an ordinary annuity. If the investment account earns 6% annually, how long will her portfolio last? Use a calculator to determine your answer.
A) 11.43 years
B) 14.17 years
C) 19.86 years
D) 23.08 years

Accepted Answer

To determine how long Marie's portfolio will last, we need to use the formula for the present value of an ordinary annuity:

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

Where:
PV = present value (in this case, $1,000,000)
PMT = yearly payment (in this case, $87,500)
r = interest rate per year (6% or 0.06)
n = number of years

We can rearrange this formula to solve for n:

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

Substituting in the values we have:

n = -log(1 - 1000000 x 0.06 / 87500) / log(1 + 0.06) = 19.86 years

Therefore, Marie's portfolio will last for 19.86 years if she spends $87,500 per year and earns 6% interest annually.

Question 9

Your need to repay a loan with a future value of $304,071.00 in 18.5 years. If you can make annual year-end deposits of $11,000 into an account, what annual rate of return would you require to earn enough money to pay the loan in full at the due date?
A) 7.92%
B) 8.73%
C) 4.16%
D) 4.39%

Accepted Answer

The answer of Your need to repay a loan with...

Question 10

Your firm intends to finance the purchase of a new construction crane. The cost is $1,500,000. How large is the payment at the end of year ten if the crane is financed at a rate of 8.50% as a discount loan?
A) $228,611.56
B) $127,500
C) $3,391,475.16
D) There is not enough information to answer this question.

Accepted Answer

In a discount loan, the interest is deducted from the principal upfront. The future value of the loan at the end of year ten can be calculated using the formula for compound interest: FV = P(1 + r)^n, where P is the principal ($1,500,000), r is the interest rate (8.50%), and n is the number of years (10). This results in a future value of $3,391,475.16.

Question 11

You have saved $47,000 for college and wish to use $15,000 per year. If you use the money as an ordinary annuity and earn 6.15% on your investment, how many years will your annuity last? Use a calculator to determine your answer.
A) 4.27 years
B) 3.13 years
C) 3.59 years
D) 3.36 years

Accepted Answer

Using the formula for the present value of an annuity, we can find the number of years, n:
$47,000 = $15,000[(1-(1+i)^{-n})/i]
Simplifying this equation, we get:
(1-(1+i)^{-n})/i = 47,000/15,000
(1-(1.0615)^{-n})/0.0615 = 3.13
1-(1.0615)^{-n} = 0.191295
(1.0615)^{-n} = 0.808705
-n*log(1.0615) = log(0.808705)
n = log(0.808705)/log(1.0615) = 3.59 
Therefore, the annuity will last for approximately 3.59 years, which is closest to choice C, 3.59 years.

Question 12

The first interest payment on a 5-year, 8%, $100,000, fully-amortized loan with annual payments will be less than the last interest payment.

Accepted Answer

The interest portion of each payment decreases over time as the loan is paid off, so the first interest payment will be higher than the last interest payment.

Question 13

The last interest payment on a 12-year, 6%, $138,000, fully-amortized loan with annual payments will be less than the first interest payment.

Accepted Answer

In a fully amortized loan, the payments are structured so that the amount of interest decreases over time as the principal is paid down, making the last interest payment less than the first.

Question 14

If you borrow $5,000 at an annual interest rate of 9.0% for six years, what will your repayment(s) be if this is an interest-only loan?

Accepted Answer

The answer of If you borrow $5,000 at an annual...

Question 15

Which of the following is NOT true with regard to an amortization table?
A) The interest payment for a period is equal to the periodic interest rate multiplied by the beginning-of-the-period principal balance.
B) The remaining principal balance at the end of a payment period is equal to the beginning-of-the-period principal less the total payment.
C) The total payment is calculated by using the present value of an annuity formula.
D) All of the above are true.

Accepted Answer

The remaining principal balance at the end of a payment period is equal to the beginning-of-the-period principal balance less the principal portion of the payment for that period, not less the total payment. The total payment includes both principal and interest components.

Question 16

Your firm intends to finance the purchase of a new construction crane. The cost is $1,500,000. What is the size of the first payment if the crane is financed with an interest-only loan at an annual rate of 8.50%?
A) $228,611.56
B) $127,500
C) $3,391,475.16
D) There is not enough information to answer this question.

Accepted Answer

An interest-only loan means that the borrower only pays the interest on the loan for a certain period of time, without reducing the principal. Therefore, the first payment would equal the annual interest due on the loan, which is (0.085 x $1,500,000) = $127,500.

Question 17

If you borrow $5,000 at an annual interest rate of 9.0% for six years, what will your repayment(s) be if this is a discount loan?

Accepted Answer

The answer of If you borrow $5,000 at an annual...

Question 18

Which of the following is NOT true regarding the total payment in an equal payment amortization table?
A) The total payment for any period is equal to the principal plus interest payments for that same period.
B) The total payment is calculated using the present value of an annuity formula rearranged to solve for the payment.
C) The final total payment will be greater than the beginning principal for the final period, assuming a positive interest rate.
D) All of the above are true.

Accepted Answer

All of the statements are true regarding the total payment in an equal payment amortization table.

Question 19

You currently have $67,000 in an interest-earning account. From this account, you wish to make 20 year-end payments of $5,000 each. What annual rate of return must you make on this account to meet your objective?
A) 4.16%
B) 5.03%
C) 6.42%
D) 7.32%

Accepted Answer

To calculate the required annual rate of return, we can use the present value of an annuity formula:
PV = PMT * ((1 - (1 + r)^-n) / r)
Where:
PV = present value (amount in the account)
PMT = payment amount ($5,000)
r = annual interest rate
n = number of payments (20)
We can plug in the given numbers and solve for r:
$67,000 = $5,000 * ((1 - (1 + r)^-20) / r)
Solving for r using a financial calculator or spreadsheet, we get r = 4.16%.
Therefore, the best choice is A) 4.16% because it is the calculated annual rate of return required to make the 20 year-end payments of $5,000 each from the existing account balance of $67,000.

Question 20

Your firm intends to finance the purchase of a new construction crane. The cost is $1,500,000. What is the size of the annual ordinary annuity payment if the loan is amortized over a ten-year period at a rate of 8.50%?
A) $228,611.56
B) $127,500
C) $3,391,475.16
D) There is not enough information to answer this question.

Accepted Answer

The formula for calculating the size of the annual ordinary annuity payment is:
PMT = (P*r)/(1-(1+r)^(-n))
Where:
P = the present value (in this case, the cost of the crane = $1,500,000)
r = the interest rate per period (8.50%/year)
n = the number of periods (10 years)
PMT = the size of the annuity payment
Plugging in the values, we get:
PMT = (1,500,000 * 0.085)/(1-(1+0.085)^(-10)) = $228,611.56
Therefore, the size of the annual ordinary annuity payment is $228,611.56. So, the best choice is A.

Quiz 4: The Time Value of Money Part 2

Assume a five-year equal payment amortization schedule with an annual interest rate of 12% and annual payments. If the beginning principal is $8,000, then the first interest payment will be how large?

Amortization tables are common and can be used for all but which of the following?

Your parents have an investment portfolio of $400,000, and they wish to take out cash flows of $50,000 per year as an ordinary annuity. How long will their portfolio last if the portfolio is invested at an annual rate of 4.50%? Use a calculator to determine your answer.

You have a choice among three types of loan and wish to pay the LEAST total cash flows. An amortized loan will result in fewer dollars paid out than a discount or an interest-only loan for the same amount, positive interest rate, and time period.

Once you begin making payments on an amortization schedule for a loan such as a mortgage or car loan, most contracts clearly state that you may NOT pay off the loan early.

Amortization tables are useful for each of the following reasons EXCEPT:

Marie has a $1,000,000 investment portfolio and she wishes to spend $87,500 per year as an ordinary annuity. If the investment account earns 6% annually, how long will her portfolio last? Use a calculator to determine your answer.

Your need to repay a loan with a future value of $304,071.00 in 18.5 years. If you can make annual year-end deposits of $11,000 into an account, what annual rate of return would you require to earn enough money to pay the loan in full at the due date?

Your firm intends to finance the purchase of a new construction crane. The cost is $1,500,000. How large is the payment at the end of year ten if the crane is financed at a rate of 8.50% as a discount loan?

You have saved $47,000 for college and wish to use $15,000 per year. If you use the money as an ordinary annuity and earn 6.15% on your investment, how many years will your annuity last? Use a calculator to determine your answer.

The first interest payment on a 5-year, 8%, $100,000, fully-amortized loan with annual payments will be less than the last interest payment.

The last interest payment on a 12-year, 6%, $138,000, fully-amortized loan with annual payments will be less than the first interest payment.

If you borrow $5,000 at an annual interest rate of 9.0% for six years, what will your repayment(s) be if this is an interest-only loan?

Which of the following is NOT true with regard to an amortization table?

Your firm intends to finance the purchase of a new construction crane. The cost is $1,500,000. What is the size of the first payment if the crane is financed with an interest-only loan at an annual rate of 8.50%?

If you borrow $5,000 at an annual interest rate of 9.0% for six years, what will your repayment(s) be if this is a discount loan?

Which of the following is NOT true regarding the total payment in an equal payment amortization table?

You currently have $67,000 in an interest-earning account. From this account, you wish to make 20 year-end payments of $5,000 each. What annual rate of return must you make on this account to meet your objective?

Your firm intends to finance the purchase of a new construction crane. The cost is $1,500,000. What is the size of the annual ordinary annuity payment if the loan is amortized over a ten-year period at a rate of 8.50%?