a$.$ Complete an amortization schedule for a $$36,000$ loan to be repaid in equal installments at the end of each of the next three years. The interest rate is $10\%$ compounded annually. Round all answers to the nearest cent.

Beginning Repayment Ending

Year Balance Payment Interest of Principal Balance

$1$ $ fill in the blank $2$

$ fill in the blank $3$

$ fill in the blank $4$

$ fill in the blank $5$

$ fill in the blank $6$

$2$ $ fill in the blank $7$

$ fill in the blank $8$

$ fill in the blank $9$

$ fill in the blank $10$

$ fill in the blank $11$

$3$ $ fill in the blank $12$

$ fill in the blank $13$

$ fill in the blank $14$

$ fill in the blank $15$

$ fill in the blank $16$

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 $1$: fill in the blank $17$

$\%$ fill in the blank $18$

$\%$

Year $2$: fill in the blank $19$

$\%$ fill in the blank $20$

$\%$

Year $3$: fill in the blank $21$

$\%$ fill in the blank $22$

$\%$

c$.$ Why do these percentages change over time?

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.

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.

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.

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.

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