Question

An amount of $200,000 is borrowed for 5 years at a rate of 12%. Make an amortization schedule showing the quarterly payment, the quarterly interest on the outstanding balance, the portion of the payment going toward reducing the debt, and the balance.

Answer 1

Step-1:Calculation of quarterly payment
Quarterly payment		=	Loan amount	/	Present value of annuity of 1
		=	$ 2,00,000.00	/	14.87747486
		=	$     13,443.14
Working:
Present value of annuity of 1		=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.03)^-20)/0.03		i	=	12%/4	=	0.03
		=	14.87747486		n	=	5*4	=	20
Step-2:Calculation of amortization schedule
Quarter	Beginning Loan		Interest Expense	Quarterly Payment	Reduction of debt	Ending Loan
	a		b=a*0.03	c	d=c-b	e=a-d
1	$ 2,00,000.00		$       6,000.00	$     13,443.14	$       7,443.14	$ 1,92,556.86
2	$ 1,92,556.86		$       5,776.71	$     13,443.14	$       7,666.44	$ 1,84,890.42
3	$ 1,84,890.42		$       5,546.71	$     13,443.14	$       7,896.43	$ 1,76,993.99
4	$ 1,76,993.99		$       5,309.82	$     13,443.14	$       8,133.32	$ 1,68,860.67
5	$ 1,68,860.67		$       5,065.82	$     13,443.14	$       8,377.32	$ 1,60,483.35
6	$ 1,60,483.35		$       4,814.50	$     13,443.14	$       8,628.64	$ 1,51,854.71
7	$ 1,51,854.71		$       4,555.64	$     13,443.14	$       8,887.50	$ 1,42,967.21
8	$ 1,42,967.21		$       4,289.02	$     13,443.14	$       9,154.13	$ 1,33,813.08
9	$ 1,33,813.08		$       4,014.39	$     13,443.14	$       9,428.75	$ 1,24,384.34
10	$ 1,24,384.34		$       3,731.53	$     13,443.14	$       9,711.61	$ 1,14,672.72
11	$ 1,14,672.72		$       3,440.18	$     13,443.14	$     10,002.96	$ 1,04,669.76
12	$ 1,04,669.76		$       3,140.09	$     13,443.14	$     10,303.05	$     94,366.72
13	$     94,366.72		$       2,831.00	$     13,443.14	$     10,612.14	$     83,754.58
14	$     83,754.58		$       2,512.64	$     13,443.14	$     10,930.50	$     72,824.07
15	$     72,824.07		$       2,184.72	$     13,443.14	$     11,258.42	$     61,565.65
16	$     61,565.65		$       1,846.97	$     13,443.14	$     11,596.17	$     49,969.48
17	$     49,969.48		$       1,499.08	$     13,443.14	$     11,944.06	$     38,025.42
18	$     38,025.42		$       1,140.76	$     13,443.14	$     12,302.38	$     25,723.04
19	$     25,723.04		$           771.69	$     13,443.14	$     12,671.45	$     13,051.59
20	$     13,051.59		$           391.55	$     13,443.14	$     13,051.59	$              -0.00
Total			$     68,862.83	$ 2,68,862.83	$ 3,37,725.66