Question 1

Golden Dragon Restaurant obtained a $9000 loan at 9% compounded annually to replace some kitchen equipment. Prepare a complete amortization schedule if the loan is to be repaid by semiannual payments over a three-year term. Calculate the total interest charges.

Accepted Answer

$1436.7

Question 2

Valley Produce received $50,000 in vendor financing at 7.8% compounded semiannually for the purchase of harvesting machinery. The contract requires equal annual payments for seven years to repay the debt. Construct the amortization schedule for the debt. How much interest will be paid over the seven-year term?

Accepted Answer

$17,115.2

Question 3

Dr. Alvano borrowed $8000 at 8% compounded quarterly to purchase a new X-Ray machine for his clinic. The agreement requires quarterly payments during a two-year amortization period. Suppose that the loan permits an additional prepayment of principal on any scheduled payment date. Prepare an amortization schedule that reflects a prepayment of $1500 with the third scheduled payment.

Accepted Answer

To prepare an amortization schedule for Dr. Alvano's loan, we need to calculate the regular quarterly payment first and then adjust the schedule to reflect the additional prepayment of $1500 with the third scheduled payment.

The loan details are as follows:
- Principal (P): $8000
- Annual interest rate (r): 8% or 0.08
- Compounding frequency: Quarterly
- Amortization period: 2 years (or 8 quarters)

The formula to calculate the regular quarterly payment (R) is given by the annuity formula for compounded interest:

R = P * [i / (1 - (1 + i)^(-n))]

Where:
- i is the quarterly interest rate (annual rate divided by the number of compounding periods per year)
- n is the total number of payments (amortization period in quarters)

First, let's calculate the quarterly interest rate and the total number of payments:

i = 0.08 / 4 = 0.02 (2% per quarter)
n = 2 * 4 = 8 quarters

Now, we can calculate the regular quarterly payment (R):

R = 8000 * [0.02 / (1 - (1 + 0.02)^(-8))]
R = 8000 * [0.02 / (1 - 1.02^(-8))]
R = 8000 * [0.02 / (1 - 0.8535)]
R = 8000 * [0.02 / 0.1465]
R = 8000 * 0.1365
R = 1092.04 (rounded to two decimal places)

Dr. Alvano's regular quarterly payment is approximately $1092.04.

Now, let's prepare the amortization schedule. We'll calculate the interest and principal components of each payment and adjust the third payment to include the additional $1500 prepayment.

| Payment # | Beginning Balance | Payment | Interest | Principal | Additional Prepayment | Ending Balance |
|-----------|-------------------|---------|----------|-----------|-----------------------|----------------|
| 1         | $8000.00          | $1092.04| $160.00  | $932.04   | $0.00                 | $7067.96       |
| 2         | $7067.96          | $1092.04| $141.36  | $950.68   | $0.00                 | $6117.28       |
| 3         | $6117.28          | $1092.04| $122.35  | $969.69   | $1500.00              | $3647.59       |
| 4         | $3647.59          | $1092.04| $72.95   | $1019.09  | $0.00                 | $2628.50       |
| ...       | ...               | ...     | ...      | ...       | ...                   | ...            |
| 8         | ...               | ...     | ...      | ...       | ...                   | $0.00          |

Note: The interest for each payment is calculated by multiplying the beginning balance by the quarterly interest rate (2%). The principal for each payment is the total payment minus the interest. The ending balance is the beginning balance minus the principal and any additional prepayment.

After the third payment, the remaining balance and the regular payment amount may change due to the prepayment. We would need to recalculate the regular payment amount based on the new balance after the prepayment, or we could continue with the same payment amount and the loan would be paid off earlier than originally scheduled.

For simplicity, I've shown the calculations for the first three payments and the fourth payment after the prepayment. The remaining payments would continue in a similar fashion until the loan is fully amortized.

Please note that the actual amortization schedule would need to be recalculated after the prepayment to reflect the new balance and potentially adjusted payment amounts or amortization period. The calculations above are simplified and rounded for illustrative purposes.

Question 4

Jean and Walter Pereira financed the addition of a swimming pool using a $24,000 home improvement loan from their bank. Monthly payments were based on an interest rate of 7.2% compounded semiannually and a five-year amortization. Construct a partial amortization schedule showing details of the first two payments, Payments 30 and 31, and the last two payments. What total interest will the Pereiras pay over the life of the loan?

Accepted Answer

The answer of Jean and Walter Pereira financed the addition...

Question 5

Golden Dragon Restaurant obtained a $9000 loan at 12.75% compounded annually to replace some kitchen equipment. Prepare a complete amortization schedule if payments of $1800 (except for a smaller final payment) are made semiannually.

Accepted Answer

The answer of Golden Dragon Restaurant obtained a $9000 loan...

Question 6

Valley Produce received $50,000 in vendor financing at 7.8% compounded semiannually for the purchase of harvesting machinery. The contract requires annual payments of $10,000 (except for a smaller final payment). Construct the complete amortization schedule for the debt. How much interest will be paid over the entire life of the loan?

Accepted Answer

The answer of Valley Produce received $50,000 in vendor financing...

Question 7

Dr. Alvano borrowed $8000 at 8% compounded quarterly to purchase a new X-Ray machine for his clinic. The agreement requires quarterly payments during a two-year amortization period. Suppose that the loan permits an additional prepayment of principal on any scheduled payment date. Prepare an amortization schedule that reflects a prepayment of $1000 with the third scheduled payment.

Accepted Answer

The answer of Dr. Alvano borrowed $8000 at 8% compounded...

Question 8

Jean and Walter Pereira financed the addition of a swimming pool using a $24,000 home improvement loan from their bank. Monthly payments of $500 (except for a smaller final payment) include interest at 7.2% compounded semiannually. Construct a partial amortization schedule showing details of the first two payments, Payments 28 and 29, and the last two payments. What total interest will the Pereiras pay over the life of the loan?

Accepted Answer

The answer of Jean and Walter Pereira financed the addition...

Question 9

Using the Loan Amortization Chart Follow the instructions in the NET @ssets box at the beginning of Section 14.1 for accessing and using the Loan Amortization Chart in this student textbook's Online Learning Centre. Enter $10,000 for the "Loan amount"and 7.5% for the monthly compounded "Interest rate."
a) Compare the profiles of the bar charts for loan terms of 30 months and 30 years. Approximately what percentage of the original principal is paid off midway through the term in each case?
b) Prepare a table presenting the total interest paid over the life of the loan for terms of 5, 10, 15, 20, 25, and 30 years.
c) Next, vary the "Term in months"
to find the term for which the total interest paid over the life of the loan equals: (i) the original principal, and (ii) 1.5 times the original principal.

Accepted Answer

The answer of Using the Loan Amortization Chart Follow the...

Question 10

Using the Loan Amortization Chart Follow the instructions in the NET @ssets box at the beginning of Section 14.1 for accessing and using the Loan Amortization Chart in this student textbook's Online Learning Centre. Use this chart and its associated report to solve:
a) Monica bought a $1250 stereo system for 20% down, with the balance to be paid with interest at 15%compounded monthly in six equal monthly payments. Construct the full amortization schedule for the debt. Calculate the total interest paid.

Accepted Answer

The answer of Using the Loan Amortization Chart Follow the...

Question 11

Will a loan's balance midway through its amortization period be (pick one): (i) more than (ii) less than or (iii) equal to half of the original principal? Explain.

Accepted Answer

The answer of Will a loan's balance midway through its...

Question 12

A loan has a 10-year amortization period. If the interest rate is fixed, will the principal repaid in the third year be (pick one): (i) more than (ii) less than or (iii) equal to the principal repaid in the seventh year? Explain.

Accepted Answer

The answer of A loan has a 10-year amortization period....

Question 13

A loan has a five-year amortization period. If the interest rate is fixed, will the interest paid in the 4^th year be (pick one): (i) more than (ii) less than or (iii) equal to the interest paid in the second year? Explain.

Accepted Answer

The answer of A loan has a five-year amortization period....

Question 14

Loan A is for $20,000 while Loan B is for $10,000. Both have the same interest rate and amortization period. Will the total interest paid on Loan A be (pick one): (i) more than (ii) less than or (iii) equal to twice the total interest paid on Loan B? Explain.

Accepted Answer

The answer of Loan A is for $20,000 while Loan...

Question 15

The interest rate on a $14,000 loan is 8.4% compounded semiannually. Semiannual payments will pay off the loan in seven years.
a) Calculate the interest component of Payment 10.
b) Calculate the principal component of Payment 3.
c) Calculate the interest paid in Year 6.
d) How much do Payments 3 to 6 inclusive reduce the principal balance?

Accepted Answer

The answer of The interest rate on a $14,000 loan...

Question 16

Elkford Logging's bank will fix the interest rate on a $60,000 loan at 8.1% compounded monthly for the first four-year term of an eight-year amortization period. Monthly payments are required on the loan.
a) If the prevailing interest rate on four-year loans at the beginning of the second term is 7.5% compounded monthly, what will be the monthly payments for the last four years?
b) What will be the interest portion of the twenty-third payment?
c) Calculate the principal portion of the fifty-third payment

Accepted Answer

The answer of Elkford Logging's bank will fix the interest...

Question 17

Christina has just borrowed $12,000 at 9% compounded semiannually. Since she expects to receive a $10,000 inheritance in two years when she turns 25, she has arranged with her credit union to make monthly payments that will reduce the principal balance to exactly $10,000 in two years.
a) What monthly payments will she make?
b) What will be the interest portion of the ninth payment?
c) Determine the principal portion of the sixteenth payment.

Accepted Answer

The answer of Christina has just borrowed $12,000 at 9%...

Question 18

Using the Loan Amortization Chart Follow the instructions in the NET @ssets box at the beginning of Section 14.1 for accessing and using the Loan Amortization Chart in this textbook's Online Learning Centre (OLC). Use this chart and its associated report to solve:
Ms. Esperanto obtained a $40,000 home equity loan at 7.5% compounded monthly.
a) What will she pay monthly if the amortization period is 15 years?
b) How much of the payment made at the end of the fifth year will go towards principal and how much will go towards interest?
c) What will be the balance on the loan after five years?
d) How much interest did she pay during the fifth year?

Accepted Answer

The answer of Using the Loan Amortization Chart Follow the...

Question 19

Elkford Logging's bank will fix the interest rate on a $60,000 loan at 8.1% compounded monthly for the first four-year term of an eight-year amortization period. Monthly payments are required on the loan.
a) If the prevailing interest rate on four-year loans at the beginning of the second term is 7.5% compounded monthly, what will be the monthly payments for the last four years?
b) What will be the interest portion of the twenty-third payment?
c) Calculate the principal portion of the fifty-third payment

Accepted Answer

The answer of Elkford Logging's bank will fix the interest...

Question 20

Using the Composition of Loan Payments Chart An interactive chart for investigating the composition of loan payments is provided in the student textbook's Online Learning Centre (OLC). Go to the Student Edition of the OLC. In the navigation bar, select "Chapter 14" in the drop-down box. In the list of resources for Chapter 14, select "Links in Student textbook" and then click on the link named "Composition of Loan Payments." The chart provides cells for entering the essential information about a loan (PV, j, m, PMT, and payments/year). You can then compare the composition (interest and principal components) of any two payments. Simply enter the serial numbers of the two payments and then click on the "Submit" button. Two bar diagrams provide a visual comparison of the interest and principal components. The actual numerical values are also displayed. Consider a $120,000 mortgage loan at 6.5% compounded semiannually. Monthly payments of $800 will pay off the loan in 25 years and 4 months. a) How much more interest is paid by the 20^th payment than the 220^th payment? b) How long does it take before the interest component of a payment drops below 50%? c) Which payment number is closest to being comprised of: (i) 75% interest? (ii) 25%interest? d) Which payment number comes closest to having a mix of principal and interest that is the opposite of the first payment's mix? e) Which payment number comes closest to having double the principal component of the 5^th payment? f) Which payment number comes closest to having half the interest component of the 10^th payment?

Accepted Answer

The answer of Using the Composition of Loan Payments Chart...

Quiz 14: Loan Amortization: Mortgages

Golden Dragon Restaurant obtained a $9000 loan at 9% compounded annually to replace some kitchen equipment. Prepare a complete amortization schedule if the loan is to be repaid by semiannual payments over a three-year term. Calculate the total interest charges.

Golden Dragon Restaurant obtained a $9000 loan at 12.75% compounded annually to replace some kitchen equipment. Prepare a complete amortization schedule if payments of $1800 (except for a smaller final payment) are made semiannually.

Will a loan's balance midway through its amortization period be (pick one): (i) more than (ii) less than or (iii) equal to half of the original principal? Explain.

A loan has a 10-year amortization period. If the interest rate is fixed, will the principal repaid in the third year be (pick one): (i) more than (ii) less than or (iii) equal to the principal repaid in the seventh year? Explain.

A loan has a five-year amortization period. If the interest rate is fixed, will the interest paid in the 4th year be (pick one): (i) more than (ii) less than or (iii) equal to the interest paid in the second year? Explain.

Loan A is for $20,000 while Loan B is for $10,000. Both have the same interest rate and amortization period. Will the total interest paid on Loan A be (pick one): (i) more than (ii) less than or (iii) equal to twice the total interest paid on Loan B? Explain.

A loan has a five-year amortization period. If the interest rate is fixed, will the interest paid in the 4^th year be (pick one): (i) more than (ii) less than or (iii) equal to the interest paid in the second year? Explain.