Question

9. Statue Builders, Inc. took out a loan for $65,000 that has to be repaid in 10 equal annual installments. The APR on the loan is 7.25%. How much of the second payment is interest? a) $4,814.22 b) $4,712.50 c) $4,375.43 d) $4,013.92 e) $9,361.77

PLEASE SHOW ALL WORK

Answer 1

c) $4,375.43

Step-1:Calculation of annual payment
Annual payment	=	Loan amount	/	Present value of annuity of 1
	=	$       65,000	/	6.943128474
	=	$   9,361.77
Working;
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.0725)^-10)/0.0725		i	=	7.25%
	=	6.94312847		n	=	10
Step-2:Calculation of interest in second payment
Interest payment		$   4,375.43
Working:
Year ended	Beginning Loan amount	Interest Expense	Annual payment	Reduction of principal	Ending Loan amount
	a	b=a*7.25%	c	d=c-b	e=a-d
1	$ 65,000.00	$   4,712.50	$ 9,361.77	$    4,649.27	$ 60,350.73
2	$ 60,350.73	$   4,375.43	$ 9,361.77	$    4,986.35	$ 55,364.38
3	$ 55,364.38	$   4,013.92	$ 9,361.77	$    5,347.86	$ 50,016.52
4	$ 50,016.52	$   3,626.20	$ 9,361.77	$    5,735.58	$ 44,280.95
5	$ 44,280.95	$   3,210.37	$ 9,361.77	$    6,151.41	$ 38,129.54
6	$ 38,129.54	$   2,764.39	$ 9,361.77	$    6,597.38	$ 31,532.16
7	$ 31,532.16	$   2,286.08	$ 9,361.77	$    7,075.69	$ 24,456.47
8	$ 24,456.47	$   1,773.09	$ 9,361.77	$    7,588.68	$ 16,867.79
9	$ 16,867.79	$   1,222.91	$ 9,361.77	$    8,138.86	$     8,728.93
10	$   8,728.93	$       632.85	$ 9,361.77	$    8,728.93	$ 0.00