Question

3) You just bought a house for $200,000. You have agreed to make 5 payments at the end of the year for 5 years with an interest rate of 6%. What will the annual payment be? Create a loan amortization schedule.

	beginning balance	payment	interest	principal	ending balance
1
						2
3
						4
5

Answer 1

Formula for Equal Annual payment:

Annual payment = (r x P)/ [1-(1+r)^-n]

P = Principal of loan = $ 200,000

r = Rate of interest = 6 % or 0.06 p.a.

n = No. of periods = 5

Substituting the values, we get annual payment as:

Annual payment = (0.06 x $ 200,000)/ [1-(1+0.06)^-5]

                              = $ 12,000/ [1-(1.06)^-5]

                              = $ 12,000/ (1-0.74725817287)

                              = $ 12,000/ 0.25274182713

                             = $ 47,479.2800869786 or $ 47,479.28

Amortization schedule:

	Beginning balance (B)	Payment (EYI)	Interest (I=B x 0.06)	Principal (P=EYI-I)	Ending balance (E=B-P)
1	$200,000.00	$47,479.28	$12,000.00	$35,479.28	$164,520.72
2	$164,520.72	$47,479.28	$9,871.24	$37,608.04	$126,912.68
3	$126,912.68	$47,479.28	$7,614.76	$39,864.52	$87,048.16
4	$87,048.16	$47,479.28	$5,222.89	$42,256.39	$44,791.77
5	$44,791.77	$47,479.28	$2,687.51	$44,791.77	$0.00