Question

a. Complete an amortization schedule for a $38,000 loan to be repaid in equal installments at the end of each of the next three years. The interest rate is 12% compounded annually. Round all answers to the nearest cent.

Beginning Balance -Payment -Interest -Repayment of Principal -Ending Balance

1 $ $ $ $ $

2 $ $ $ $ $

3 $ $ $ $ $

b. What percentage of the payment represents interest and what percentage represents principal for each of the three years? Round all answers to two decimal places.

% Interest- % Principal

Year 1: % %

Year 2: % %

Year 3: % %

c. Why do these percentages change over time? (pick one)

1. These percentages change over time because even though the total payment is constant the amount of interest paid each year is declining as the remaining or outstanding balance declines.

2. These percentages change over time because even though the total payment is constant the amount of interest paid each year is increasing as the remaining or outstanding balance declines.

3. These percentages change over time because even though the total payment is constant the amount of interest paid each year is declining as the remaining or outstanding balance increases.

4. These percentages change over time because even though the total payment is constant the amount of interest paid each year is increasing as the remaining or outstanding balance increases.

5. These percentages do not change over time; interest and principal are each a constant percentage of the total payment.

Answer 1

c. Why do these percentages change over time?

The correct answer is:

Option 1. These percentages change over time because even though the total payment is constant the amount of interest paid each year is declining as the remaining or outstanding balance declines.

As can be seen above, the annual payment includes both interest and principal and interest is calculated on the declining balance. Thus, the interest portion is higher in initial years gradually reducing in subsequent years.

The other options are incorrect because:

Option 2: The amount of interest paid each year is mentioned as increasing which is incorrect as interest paid each year reduces.

Option 3. The amount of outstanding balance is mentioned as increasing which is incorrect as outstanding balance each year reduces.

Option 4: The amount of interest paid each year and also amount of outstanding balance is mentioned as increasing which is incorrect as both interest paid and amount of outstanding balance each year reduces.

Option 5: It is mentioned that these percentages do not change over time which is incorrect as both the percentages changes in all the years.

Workings: