Question

CTL (Concrete Testing Lab) borrowed $120,000 for new equipment at 12% per year, compounded quarterly. It is to be paid back over 4 years in equal quarterly payments.

How much interest is in the 6th payment? $

How much principal is in the 6th payment? $

What principal is owed immediately following the 6th payment?

Answer 1

(a) Interest in the 6th payment is $ 2,651.79

(b) Principal in the 6th payment is $ 6,901.51

(c) Principal owed immediately following the 6th payment is $ 81,491.60

Step-1:Calculation of quarterly payment
Quarterly payment	=	Loan amount	/	Present Value of annuity of 1
	=	$ 1,20,000.00	/	12.561102
	=	$       9,553.30
Working:
Present Value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.03)^-16)/0.03		i	=	12%/4	=	0.03
	=	12.56110203		n	=	4*4	=	16
Step-2:Loan amortization Schedule
Quarter ended	Loan amount	Interest Expense	Quarterly payment	Reduction of principal	Ending Loan amount
	a	b=a*0.03	c	d=c-b	e=a-d
1	$ 1,20,000.00	$       3,600.00	$ 9,553.30	$ 5,953.30	$ 1,14,046.70
2	$ 1,14,046.70	$       3,421.40	$ 9,553.30	$ 6,131.90	$ 1,07,914.80
3	$ 1,07,914.80	$       3,237.44	$ 9,553.30	$ 6,315.86	$ 1,01,598.94
4	$ 1,01,598.94	$       3,047.97	$ 9,553.30	$ 6,505.33	$     95,093.61
5	$     95,093.61	$       2,852.81	$ 9,553.30	$ 6,700.49	$     88,393.11
6	$     88,393.11	$       2,651.79	$ 9,553.30	$ 6,901.51	$     81,491.60