Question

A：
You are the finance manager of your company. Your company is planning for capacity expansion and need to borrow RM850,000 from a local bank. The offered term loan will be amortised in 9 years with a nomimal interest rate of 7.2% p.a. compounded monthly. The final payment will be at the end of Year 9.

1.Based on your working on an amortisation table, how much principal and interest would have your company paid after the first four months of payments?

If you have a choice, would you prefer to repay the above loan monthly (assume7.2% per year is compounded monthly) or annually (assume 7.2% per year is compounded annually) based on the total interest incurred? What is the main factor that contribute to such a difference in interest?

B:
You wish to retire in 20 years. Currently, your pre-retirement fund has RM50,000 in a savings account yielding 3.0% annually and RM300,000 quality stocks yielding 11.0% annually. Furthermore, you expect to add RM8,000 to the savings account and RM15,000 to your stock portfolios at the end of each year in the next 20 year. You will keep this fund until the retirement date.

1.Calculate the overall rate of return per year that you must earn on your post-retirement fund if you wish to withdraw RM240,000 at the end of each year in the following 25 years after retirement.

2.How much would your remaining fund be after three year-end withdrawals of RM 300,000 each post the retirement? Assume your fund earns a return of 5% per year.

Answer 1

Note- Change the $ symbol to RM

A.

Option-1 (Repayment of loan monthly at the end of each month)

Monthly fixed payment will be calculated as follows by Annuity method-

PV of the monthly payment =

=>

=>

=> Monthly payment= 10716.64

Payment Every Month  10,716.64

Total of 108 Payments  1,157,397.52

Total Interest  307,397.52

	Beginning Balance	[email protected]% per month on opening balance	Principal payment	Total Payment (Interest +Principal)	Ending Balance
1	$850,000.00	$5,100.00	$5,616.64	$10716.64	$844,383.36
2	$844,383.36	$5,066.30	$5,650.34	$10716.64	$838,733.01
3	$838,733.01	$5,032.40	$5,684.25	$10716.64	$833,048.77
4	$833,048.77	$4,998.29	$5,718.35	$10716.64	$827,330.42
5	$827,330.42	$4,963.98	$5,752.66	$10716.64	$821,577.75
6	$821,577.75	$4,929.47	$5,787.18	$10716.64	$815,790.58
7	$815,790.58	$4,894.74	$5,821.90	$10716.64	$809,968.68
8	$809,968.68	$4,859.81	$5,856.83	$10716.64	$804,111.85
9	$804,111.85	$4,824.67	$5,891.97	$10716.64	$798,219.87
10	$798,219.87	$4,789.32	$5,927.32	$10716.64	$792,292.55
11	$792,292.55	$4,753.76	$5,962.89	$10716.64	$786,329.66
12	$786,329.66	$4,717.98	$5,998.67	$10716.64	$780,330.99
Year #1 End
13	$780,330.99	$4,681.99	$6,034.66	$10716.64	$774,296.34
14	$774,296.34	$4,645.78	$6,070.87	$10716.64	$768,225.47
15	$768,225.47	$4,609.35	$6,107.29	$10716.64	$762,118.18
16	$762,118.18	$4,572.71	$6,143.93	$10716.64	$755,974.25
17	$755,974.25	$4,535.85	$6,180.80	$10716.64	$749,793.45
18	$749,793.45	$4,498.76	$6,217.88	$10716.64	$743,575.56
19	$743,575.56	$4,461.45	$6,255.19	$10716.64	$737,320.37
20	$737,320.37	$4,423.92	$6,292.72	$10716.64	$731,027.65
21	$731,027.65	$4,386.17	$6,330.48	$10716.64	$724,697.18
22	$724,697.18	$4,348.18	$6,368.46	$10716.64	$718,328.71
23	$718,328.71	$4,309.97	$6,406.67	$10716.64	$711,922.04
24	$711,922.04	$4,271.53	$6,445.11	$10716.64	$705,476.93
Year #2 End
25	$705,476.93	$4,232.86	$6,483.78	$10716.64	$698,993.15
26	$698,993.15	$4,193.96	$6,522.68	$10716.64	$692,470.46
27	$692,470.46	$4,154.82	$6,561.82	$10716.64	$685,908.64
28	$685,908.64	$4,115.45	$6,601.19	$10716.64	$679,307.45
29	$679,307.45	$4,075.84	$6,640.80	$10716.64	$672,666.65
30	$672,666.65	$4,036.00	$6,680.64	$10716.64	$665,986.01
31	$665,986.01	$3,995.92	$6,720.73	$10716.64	$659,265.28
32	$659,265.28	$3,955.59	$6,761.05	$10716.64	$652,504.23
33	$652,504.23	$3,915.03	$6,801.62	$10716.64	$645,702.61
34	$645,702.61	$3,874.22	$6,842.43	$10716.64	$638,860.18
35	$638,860.18	$3,833.16	$6,883.48	$10716.64	$631,976.70
36	$631,976.70	$3,791.86	$6,924.78	$10716.64	$625,051.92
Year #3 End
37	$625,051.92	$3,750.31	$6,966.33	$10716.64	$618,085.59
38	$618,085.59	$3,708.51	$7,008.13	$10716.64	$611,077.46
39	$611,077.46	$3,666.46	$7,050.18	$10716.64	$604,027.28
40	$604,027.28	$3,624.16	$7,092.48	$10716.64	$596,934.80
41	$596,934.80	$3,581.61	$7,135.03	$10716.64	$589,799.76
42	$589,799.76	$3,538.80	$7,177.85	$10716.64	$582,621.92
43	$582,621.92	$3,495.73	$7,220.91	$10716.64	$575,401.00
44	$575,401.00	$3,452.41	$7,264.24	$10716.64	$568,136.77
45	$568,136.77	$3,408.82	$7,307.82	$10716.64	$560,828.94
46	$560,828.94	$3,364.97	$7,351.67	$10716.64	$553,477.27
47	$553,477.27	$3,320.86	$7,395.78	$10716.64	$546,081.49
48	$546,081.49	$3,276.49	$7,440.15	$10716.64	$538,641.34
Year #4 End
49	$538,641.34	$3,231.85	$7,484.80	$10716.64	$531,156.54
50	$531,156.54	$3,186.94	$7,529.70	$10716.64	$523,626.84
51	$523,626.84	$3,141.76	$7,574.88	$10716.64	$516,051.96
52	$516,051.96	$3,096.31	$7,620.33	$10716.64	$508,431.62
53	$508,431.62	$3,050.59	$7,666.05	$10716.64	$500,765.57
54	$500,765.57	$3,004.59	$7,712.05	$10716.64	$493,053.52
55	$493,053.52	$2,958.32	$7,758.32	$10716.64	$485,295.20
56	$485,295.20	$2,911.77	$7,804.87	$10716.64	$477,490.32
57	$477,490.32	$2,864.94	$7,851.70	$10716.64	$469,638.62
58	$469,638.62	$2,817.83	$7,898.81	$10716.64	$461,739.81
59	$461,739.81	$2,770.44	$7,946.20	$10716.64	$453,793.61
60	$453,793.61	$2,722.76	$7,993.88	$10716.64	$445,799.72
Year #5 End
61	$445,799.72	$2,674.80	$8,041.85	$10716.64	$437,757.88
62	$437,757.88	$2,626.55	$8,090.10	$10716.64	$429,667.78
63	$429,667.78	$2,578.01	$8,138.64	$10716.64	$421,529.15
64	$421,529.15	$2,529.17	$8,187.47	$10716.64	$413,341.68
65	$413,341.68	$2,480.05	$8,236.59	$10716.64	$405,105.08
66	$405,105.08	$2,430.63	$8,286.01	$10716.64	$396,819.07
67	$396,819.07	$2,380.91	$8,335.73	$10716.64	$388,483.34
68	$388,483.34	$2,330.90	$8,385.74	$10716.64	$380,097.60
69	$380,097.60	$2,280.59	$8,436.06	$10716.64	$371,661.54
70	$371,661.54	$2,229.97	$8,486.67	$10716.64	$363,174.86
71	$363,174.86	$2,179.05	$8,537.59	$10716.64	$354,637.27
72	$354,637.27	$2,127.82	$8,588.82	$10716.64	$346,048.45
Year #6 End
73	$346,048.45	$2,076.29	$8,640.35	$10716.64	$337,408.10
74	$337,408.10	$2,024.45	$8,692.20	$10716.64	$328,715.90
75	$328,715.90	$1,972.30	$8,744.35	$10716.64	$319,971.55
76	$319,971.55	$1,919.83	$8,796.81	$10716.64	$311,174.74
77	$311,174.74	$1,867.05	$8,849.60	$10716.64	$302,325.14
78	$302,325.14	$1,813.95	$8,902.69	$10716.64	$293,422.45
79	$293,422.45	$1,760.53	$8,956.11	$10716.64	$284,466.34
80	$284,466.34	$1,706.80	$9,009.85	$10716.64	$275,456.50
81	$275,456.50	$1,652.74	$9,063.90	$10716.64	$266,392.59
82	$266,392.59	$1,598.36	$9,118.29	$10716.64	$257,274.30
83	$257,274.30	$1,543.65	$9,173.00	$10716.64	$248,101.31
84	$248,101.31	$1,488.61	$9,228.04	$10716.64	$238,873.27
Year #7 End
85	$238,873.27	$1,433.24	$9,283.40	$10716.64	$229,589.87
86	$229,589.87	$1,377.54	$9,339.10	$10716.64	$220,250.76
87	$220,250.76	$1,321.50	$9,395.14	$10716.64	$210,855.62
88	$210,855.62	$1,265.13	$9,451.51	$10716.64	$201,404.11
89	$201,404.11	$1,208.42	$9,508.22	$10716.64	$191,895.89
90	$191,895.89	$1,151.38	$9,565.27	$10716.64	$182,330.62
91	$182,330.62	$1,093.98	$9,622.66	$10716.64	$172,707.96
92	$172,707.96	$1,036.25	$9,680.40	$10716.64	$163,027.57
93	$163,027.57	$978.17	$9,738.48	$10716.64	$153,289.09
94	$153,289.09	$919.73	$9,796.91	$10716.64	$143,492.18
95	$143,492.18	$860.95	$9,855.69	$10716.64	$133,636.49
96	$133,636.49	$801.82	$9,914.82	$10716.64	$123,721.67
Year #8 End
97	$123,721.67	$742.33	$9,974.31	$10716.64	$113,747.35
98	$113,747.35	$682.48	$10,034.16	$10716.64	$103,713.19
99	$103,713.19	$622.28	$10,094.36	$10716.64	$93,618.83
100	$93,618.83	$561.71	$10,154.93	$10716.64	$83,463.90
101	$83,463.90	$500.78	$10,215.86	$10716.64	$73,248.04
102	$73,248.04	$439.49	$10,277.16	$10716.64	$62,970.88
103	$62,970.88	$377.83	$10,338.82	$10716.64	$52,632.06
104	$52,632.06	$315.79	$10,400.85	$10716.64	$42,231.21
105	$42,231.21	$253.39	$10,463.26	$10716.64	$31,767.96
106	$31,767.96	$190.61	$10,526.04	$10716.64	$21,241.92
107	$21,241.92	$127.45	$10,589.19	$10716.64	$10,652.73
108	$10,652.73	$63.92	$10,652.73	$10716.64	$0.00

After First 4 month of payment-

Total interest payment - $20196.99

Total Principal Payment - $22669.58

	Beginning Balance	[email protected]% per month on opening balance	Principal payment	Total Payment (Interest +Principal)	Ending Balance
1	$850,000.00	$5,100.00	$5,616.64	$10716.64	$844,383.36
2	$844,383.36	$5,066.30	$5,650.34	$10716.64	$838,733.01
3	$838,733.01	$5,032.40	$5,684.25	$10716.64	$833,048.77
4	$833,048.77	$4,998.29	$5,718.35	$10716.64	$827,330.42
	Total	$20196.99	$22669.58	$42866.57

Option-2 (Repayment of loan Annually at the end of each year)

Monthly fixed payment will be calculated as follows by Annuity method-

PV of the Annual payment =

=>

=>

=> Annual payment= 131575.66

Payment Every Year  $131,575.66

Total of 9 Payments  $1,184,180.97

Total Interest  $334,180.97

	Beginning Balance	[email protected]% per annum on the beginning balance	Principal	Total (Interest + Principal)	Ending Balance
1	$850,000.00	$61,200.00	$70,375.66	$131,575.66	$779,624.34
2	$779,624.34	$56,132.95	$75,442.71	$131,575.66	$704,181.63
3	$704,181.63	$50,701.08	$80,874.59	$131,575.66	$623,307.04
4	$623,307.04	$44,878.11	$86,697.56	$131,575.66	$536,609.48
5	$536,609.48	$38,635.88	$92,939.78	$131,575.66	$443,669.71
6	$443,669.71	$31,944.22	$99,631.44	$131,575.66	$344,038.26
7	$344,038.26	$24,770.75	$106,804.91	$131,575.66	$237,233.35
8	$237,233.35	$17,080.80	$114,494.86	$131,575.66	$122,738.49
9	$122,738.49	$8,837.17	$122,738.49	$131,575.66	$0.00

Analysis of payments-

	Monthly payment	Annual payment
Total Payment	$ 1,157,397.52	$1184180.97
Total Interest	$307,397.52	$334180.97

Hence mothly payment is better as the total payment and interest is less.

-------------------------------------------------------------------------------------------------------------------

B.

After 20 year Balance in Savings account-

End Balance	$305,268.56
Starting Amount	$50,000.00
Total Contributions	$160,000.00
Total Interest	$95,268.56

	start principal	start balance	interest	end balance	end principal
1	$50,000.00	$50,000.00	$1,500.00	$59,500.00	$58,000.00
2	$58,000.00	$59,500.00	$1,784.99	$69,285.00	$66,000.00
3	$66,000.00	$69,285.00	$2,078.57	$79,363.55	$74,000.00
4	$74,000.00	$79,363.55	$2,380.91	$89,744.46	$82,000.00
5	$82,000.00	$89,744.46	$2,692.34	$100,436.79	$90,000.00
6	$90,000.00	$100,436.79	$3,013.10	$111,449.89	$98,000.00
7	$98,000.00	$111,449.89	$3,343.50	$122,793.39	$106,000.00
8	$106,000.00	$122,793.39	$3,683.80	$134,477.19	$114,000.00
9	$114,000.00	$134,477.19	$4,034.33	$146,511.51	$122,000.00
10	$122,000.00	$146,511.51	$4,395.35	$158,906.85	$130,000.00
11	$130,000.00	$158,906.85	$4,767.19	$171,674.06	$138,000.00
12	$138,000.00	$171,674.06	$5,150.22	$184,824.28	$146,000.00
13	$146,000.00	$184,824.28	$5,544.73	$198,369.01	$154,000.00
14	$154,000.00	$198,369.01	$5,951.08	$212,320.08	$162,000.00
15	$162,000.00	$212,320.08	$6,369.61	$226,689.68	$170,000.00
16	$170,000.00	$226,689.68	$6,800.68	$241,490.37	$178,000.00
17	$178,000.00	$241,490.37	$7,244.71	$256,735.08	$186,000.00
18	$186,000.00	$256,735.08	$7,702.06	$272,437.14	$194,000.00
19	$194,000.00	$272,437.14	$8,173.13	$288,610.25	$202,000.00
20	$202,000.00	$288,610.25	$8,658.32	$305,268.56	$210,000.00

After20 year balance in QUALITY STOCK Account-

End Balance	$3,381,735.94
Starting Amount	$300,000.00
Total Contributions	$300,000.00
Total Interest	$2,781,735.94

	start principal	start balance	interest	end balance	end principal
1	$300,000.00	$300,000.00	$33,000.00	$348,000.00	$315,000.00
2	$315,000.00	$348,000.00	$38,280.01	$401,280.00	$330,000.00
3	$330,000.00	$401,280.00	$44,140.81	$460,420.80	$345,000.00
4	$345,000.00	$460,420.80	$50,646.30	$526,067.09	$360,000.00
5	$360,000.00	$526,067.09	$57,867.37	$598,934.47	$375,000.00
6	$375,000.00	$598,934.47	$65,882.80	$679,817.26	$390,000.00
7	$390,000.00	$679,817.26	$74,779.89	$769,597.16	$405,000.00
8	$405,000.00	$769,597.16	$84,655.68	$869,252.84	$420,000.00
9	$420,000.00	$869,252.84	$95,617.82	$979,870.66	$435,000.00
10	$435,000.00	$979,870.66	$107,785.78	$1,102,656.43	$450,000.00
11	$450,000.00	$1,102,656.43	$121,292.20	$1,238,948.64	$465,000.00
12	$465,000.00	$1,238,948.64	$136,284.36	$1,390,232.99	$480,000.00
13	$480,000.00	$1,390,232.99	$152,925.63	$1,558,158.62	$495,000.00
14	$495,000.00	$1,558,158.62	$171,397.45	$1,744,556.06	$510,000.00
15	$510,000.00	$1,744,556.06	$191,901.18	$1,951,457.23	$525,000.00
16	$525,000.00	$1,951,457.23	$214,660.31	$2,181,117.53	$540,000.00
17	$540,000.00	$2,181,117.53	$239,922.94	$2,436,040.45	$555,000.00
18	$555,000.00	$2,436,040.45	$267,964.45	$2,719,004.90	$570,000.00
19	$570,000.00	$2,719,004.90	$299,090.52	$3,033,095.44	$585,000.00
20	$585,000.00	$3,033,095.44	$333,640.52	$3,381,735.94	$600,000.00

Total withdrawl will be $240000 at the end of each year for next 25 year

Balace at the begin og 25 year=

Savings Account	$305,268.56
Quality stock	$3381735.94
Total	$3687004.50

Let the annual return is "i %''

PV of the Annual withdrawn=

=>

=>

=>(1+i)^-25 = 1- (15.3625*i)

=> i = 4.159%

hence the rate of return per year = 4.159% post retirement.

Proof-

	start principal	start balance	[email protected]%	Withdrawn	end balance	end principal
1	$3,687,005.00	$3,687,005.00	$153,349.29	$240000	$3,600,354.30	$3,447,005.00
2	$3,447,005.00	$3,600,354.30	$149,745.32	$240000	$3,510,099.63	$3,207,005.00
3	$3,207,005.00	$3,510,099.63	$145,991.48	$240000	$3,416,091.11	$2,967,005.00
4	$2,967,005.00	$3,416,091.11	$142,081.51	$240000	$3,318,172.60	$2,727,005.00
5	$2,727,005.00	$3,318,172.60	$138,008.88	$240000	$3,216,181.49	$2,487,005.00
6	$2,487,005.00	$3,216,181.49	$133,766.91	$240000	$3,109,948.37	$2,247,005.00
7	$2,247,005.00	$3,109,948.37	$129,348.45	$240000	$2,999,296.82	$2,007,005.00
8	$2,007,005.00	$2,999,296.82	$124,746.24	$240000	$2,884,043.08	$1,767,005.00
9	$1,767,005.00	$2,884,043.08	$119,952.63	$240000	$2,763,995.72	$1,527,005.00
10	$1,527,005.00	$2,763,995.72	$114,959.64	$240000	$2,638,955.37	$1,287,005.00
11	$1,287,005.00	$2,638,955.37	$109,759.00	$240000	$2,508,714.36	$1,047,005.00
12	$1,047,005.00	$2,508,714.36	$104,342.04	$240000	$2,373,056.39	$807,005.00
13	$807,005.00	$2,373,056.39	$98,699.76	$240000	$2,231,756.15	$567,005.00
14	$567,005.00	$2,231,756.15	$92,822.83	$240000	$2,084,578.98	$327,005.00
15	$327,005.00	$2,084,578.98	$86,701.46	$240000	$1,931,280.44	$87,005.00
16	$87,005.00	$1,931,280.44	$80,325.51	$240000	$1,771,605.94	-$152,995.00
17	-$152,995.00	$1,771,605.94	$73,684.33	$240000	$1,605,290.28	-$392,995.00
18	-$392,995.00	$1,605,290.28	$66,766.95	$240000	$1,432,057.24	-$632,995.00
19	-$632,995.00	$1,432,057.24	$59,561.88	$240000	$1,251,619.13	-$872,995.00
20	-$872,995.00	$1,251,619.13	$52,057.14	$240000	$1,063,676.26	-$1,112,995.00
21	-$1,112,995.00	$1,063,676.26	$44,240.24	$240000	$867,916.51	-$1,352,995.00
22	-$1,352,995.00	$867,916.51	$36,098.24	$240000	$664,014.75	-$1,592,995.00
23	-$1,592,995.00	$664,014.75	$27,617.58	$240000	$451,632.34	-$1,832,995.00
24	-$1,832,995.00	$451,632.34	$18,784.22	$240000	$230,416.55	-$2,072,995.00
25	-$2,072,995.00	$230,416.55	$9,583.43	$240000	$0.00	-$2,312,995.00

-----------

B-2

Fund balance after 3 year-

End Balance	$3,322,419.16
Starting Amount	$3,687,005.00
Total Contributions	$-900,000.00
Total Interest	$535,414.16

	start principal	start balance	interest@5%	Withdraw	end balance	end principal
1	$3,687,005.00	$3,687,005.00	$184,350.23	$300000	$3,571,355.25	$3,387,005.00
2	$3,387,005.00	$3,571,355.25	$178,567.74	$300000	$3,449,923.01	$3,087,005.00
3	$3,087,005.00	$3,449,923.01	$172,496.13	$300000	$3,322,419.16	$2,787,005.00

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