Question

3. A mortgage loan in the amount of $150,000 is arranged with annual interest 8%

compounded semi-annually. The loan is to be fully amortized in 20 years with quarterly payments. For

this exercise assume the term is also 20 years.

(a)Calculate the amount of principal paid for each of the first two quarters.

(b)What is the outstanding balance of the mortgage at the end of the 3rd year?

(c)What is the total amount of interests paid on the loan over its l

Answer 1

Using the formula:
A = P x r(1+r) ^n/(1+r) ^n – 1
Where;
A = payment Amount per period
P = initial Principal (loan amount)
r = interest rate per period
n = total number of payments or periods.
Actual Amortization Schedule which can be made for the given scenario;

	Amortization Schedule:
	$ 150,000.00 Loan with Quarterly Payments,
	8% Interest Rate -Compounded Semi-Annually,
	20 Years tenure, or 80 Quarters
Year	Quarter	Payment	Principal Paid	Interest Paid	Remaining Balance
1	1	$ 3,752.11	$ 781.52	$ 2,970.59	$ 149,218.48
	2	$ 3,752.11	$ 797.00	$ 2,955.11	$ 148,421.48
	3	$ 3,752.11	$ 812.79	$ 2,939.32	$ 147,608.69
	4	$ 3,752.11	$ 828.88	$ 2,923.23	$ 146,779.81
2	5	$ 3,752.11	$ 845.30	$ 2,906.81	$ 145,934.51
	6	$ 3,752.11	$ 862.04	$ 2,890.07	$ 145,072.47
	7	$ 3,752.11	$ 879.11	$ 2,873.00	$ 144,193.36
	8	$ 3,752.11	$ 896.52	$ 2,855.59	$ 143,296.84
3	9	$ 3,752.11	$ 914.27	$ 2,837.84	$ 142,382.57
	10	$ 3,752.11	$ 932.38	$ 2,819.73	$ 141,450.19
	11	$ 3,752.11	$ 950.84	$ 2,801.27	$ 140,499.35
	12	$ 3,752.11	$ 969.67	$ 2,782.44	$ 139,529.68
4	13	$ 3,752.11	$ 988.88	$ 2,763.23	$ 138,540.80
	14	$ 3,752.11	$ 1,008.46	$ 2,743.65	$ 137,532.34
	15	$ 3,752.11	$ 1,028.43	$ 2,723.68	$ 136,503.91
	16	$ 3,752.11	$ 1,048.80	$ 2,703.31	$ 135,455.11
5	17	$ 3,752.11	$ 1,069.57	$ 2,682.54	$ 134,385.54
	18	$ 3,752.11	$ 1,090.75	$ 2,661.36	$ 133,294.79
	19	$ 3,752.11	$ 1,112.35	$ 2,639.76	$ 132,182.44
	20	$ 3,752.11	$ 1,134.38	$ 2,617.73	$ 131,048.06
6	21	$ 3,752.11	$ 1,156.85	$ 2,595.26	$ 129,891.21
	22	$ 3,752.11	$ 1,179.76	$ 2,572.35	$ 128,711.45
	23	$ 3,752.11	$ 1,203.12	$ 2,548.99	$ 127,508.33
	24	$ 3,752.11	$ 1,226.95	$ 2,525.16	$ 126,281.38
7	25	$ 3,752.11	$ 1,251.25	$ 2,500.86	$ 125,030.13
	26	$ 3,752.11	$ 1,276.03	$ 2,476.08	$ 123,754.10
	27	$ 3,752.11	$ 1,301.30	$ 2,450.81	$ 122,452.80
	28	$ 3,752.11	$ 1,327.07	$ 2,425.04	$ 121,125.73
8	29	$ 3,752.11	$ 1,353.35	$ 2,398.76	$ 119,772.38
	30	$ 3,752.11	$ 1,380.15	$ 2,371.96	$ 118,392.23
	31	$ 3,752.11	$ 1,407.48	$ 2,344.63	$ 116,984.75
	32	$ 3,752.11	$ 1,435.36	$ 2,316.75	$ 115,549.39
9	33	$ 3,752.11	$ 1,463.78	$ 2,288.33	$ 114,085.61
	34	$ 3,752.11	$ 1,492.77	$ 2,259.34	$ 112,592.84
	35	$ 3,752.11	$ 1,522.33	$ 2,229.78	$ 111,070.51
	36	$ 3,752.11	$ 1,552.48	$ 2,199.63	$ 109,518.03
10	37	$ 3,752.11	$ 1,583.23	$ 2,168.88	$ 107,934.80
	38	$ 3,752.11	$ 1,614.58	$ 2,137.53	$ 106,320.22
	39	$ 3,752.11	$ 1,646.55	$ 2,105.56	$ 104,673.67
	40	$ 3,752.11	$ 1,679.16	$ 2,072.95	$ 102,994.51
11	41	$ 3,752.11	$ 1,712.42	$ 2,039.69	$ 101,282.09
	42	$ 3,752.11	$ 1,746.33	$ 2,005.78	$ 99,535.76
	43	$ 3,752.11	$ 1,780.91	$ 1,971.20	$ 97,754.85
	44	$ 3,752.11	$ 1,816.18	$ 1,935.93	$ 95,938.67
12	45	$ 3,752.11	$ 1,852.15	$ 1,899.96	$ 94,086.52
	46	$ 3,752.11	$ 1,888.83	$ 1,863.28	$ 92,197.69
	47	$ 3,752.11	$ 1,926.24	$ 1,825.87	$ 90,271.45
	48	$ 3,752.11	$ 1,964.38	$ 1,787.73	$ 88,307.07
13	49	$ 3,752.11	$ 2,003.29	$ 1,748.82	$ 86,303.78
	50	$ 3,752.11	$ 2,042.96	$ 1,709.15	$ 84,260.82
	51	$ 3,752.11	$ 2,083.42	$ 1,668.69	$ 82,177.40
	52	$ 3,752.11	$ 2,124.68	$ 1,627.43	$ 80,052.72
14	53	$ 3,752.11	$ 2,166.75	$ 1,585.36	$ 77,885.97
	54	$ 3,752.11	$ 2,209.66	$ 1,542.45	$ 75,676.31
	55	$ 3,752.11	$ 2,253.42	$ 1,498.69	$ 73,422.89
	56	$ 3,752.11	$ 2,298.05	$ 1,454.06	$ 71,124.84
15	57	$ 3,752.11	$ 2,343.56	$ 1,408.55	$ 68,781.28
	58	$ 3,752.11	$ 2,389.97	$ 1,362.14	$ 66,391.31
	59	$ 3,752.11	$ 2,437.30	$ 1,314.81	$ 63,954.01
	60	$ 3,752.11	$ 2,485.57	$ 1,266.54	$ 61,468.44
16	61	$ 3,752.11	$ 2,534.79	$ 1,217.32	$ 58,933.65
	62	$ 3,752.11	$ 2,584.99	$ 1,167.12	$ 56,348.66
	63	$ 3,752.11	$ 2,636.19	$ 1,115.92	$ 53,712.47
	64	$ 3,752.11	$ 2,688.39	$ 1,063.72	$ 51,024.08
17	65	$ 3,752.11	$ 2,741.63	$ 1,010.48	$ 48,282.45
	66	$ 3,752.11	$ 2,795.93	$ 956.18	$ 45,486.52
	67	$ 3,752.11	$ 2,851.30	$ 900.81	$ 42,635.22
	68	$ 3,752.11	$ 2,907.77	$ 844.34	$ 39,727.45
18	69	$ 3,752.11	$ 2,965.35	$ 786.76	$ 36,762.10
	70	$ 3,752.11	$ 3,024.08	$ 728.03	$ 33,738.02
	71	$ 3,752.11	$ 3,083.97	$ 668.14	$ 30,654.05
	72	$ 3,752.11	$ 3,145.04	$ 607.07	$ 27,509.01
19	73	$ 3,752.11	$ 3,207.32	$ 544.79	$ 24,301.69
	74	$ 3,752.11	$ 3,270.84	$ 481.27	$ 21,030.85
	75	$ 3,752.11	$ 3,335.62	$ 416.49	$ 17,695.23
	76	$ 3,752.11	$ 3,401.68	$ 350.43	$ 14,293.55
20	77	$ 3,752.11	$ 3,469.04	$ 283.07	$ 10,824.51
	78	$ 3,752.11	$ 3,537.74	$ 214.37	$ 7,286.77
	79	$ 3,752.11	$ 3,607.80	$ 144.31	$ 3,678.97
	80	$ 3,751.83	$ 3,678.97	$ 72.86	$ 0
	Totals	$ 300,168.52	$ 150,000.00	$ 150,168.52

a. Amount of principal paid for each of the first two quarters = $781.52 & $797.00.

b. Outstanding balance of the mortgage at the end of the 3rd year = $139,529.68.

c. Total amount of interests paid on the loan over its complete tenure = $150,168.52