Question

a. Complete an amortization schedule for a $44,000 loan to be repaid in equal installments at the end of each of the next three years. The interest rate is 11% compounded annually. Round all answers to the nearest cent.

	Beginning			Repayment	Ending
Year	Balance	Payment	Interest	of Principal	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?

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.

Answer 1

Step 1 : Calculation of annual installment

We have

Present value of Annuity = A*[(1-(1+r)^-n)/r]

Where

A - Annuity payment = ?

r - rate per period = 11%

n - no. of periods = 3

44,000 = A*[(1-(1.11)^-3)/.11]

= A*[(1-.731193)/.11]

= A * 2.4437

A = 44,000/2.4437

= 18,005.48

a. Amortization schedule

Year	Opening Balance	Total Payment	interest paid	principal paid	end balance
1	44000.00	18005.48	4840.00	13165.48	30834.52
2	30834.52	18005.48	3391.80	14613.68	16220.84
3	16220.84	18005.48	1784.64	16220.84	0.00

*Rounding difference of .35 is adusted with interest in year 3.

Interest Paid = Opening Balance*12%

Principal Paid = Total payment - Interest Paid

End balance = Opening Balance - Principal Paid

b.

Year	% interest		% principal
1	4840*100/18005.48	26.88	100-26.88	73.12
2	3391.80*100/18005.49	18.84	100-18.84	81.16
3	1784.64*100/18005.50	9.91	100-9.91	90.09

c. 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.