Question

USE THE INFORMATION BELOW TO ANSWER THE FOLLOWING THREE QUESTIONS

Vito Scaletta just bought his dream car, 2019 Aston Martin DB9 that cost $208,700. He paid $30,000 down and financed the balance over 84 months at 6.25% p.a. (Assume that Vito makes all required payments on time).

29. What will the balance on Vito’s loan be at the end of the fourth year (that is, immediately after Vito makes his 48th payment on the loan)?

30. What is the total amount of interest that Vito will pay over the entire term of the loan (that is, the total amount of interest that is paid on payments 1 through 84)?

31. Today is your 30th birthday and you have a dream of retiring on your 65th birthday. You want to put aside however much is necessary on your 31st through 65th birthdays (35 annual payments) to have enough to retire. You've estimated that you will live until you are 90 and you want the first withdrawal to occur on your 66th birthday, with the last payment occurring on your 90th birthday. You think that you will need $150,000 per year to spend during retirement. You estimate constant interest rates of 11.25%. Assuming that you currently have $7,500 deposited in your retirement account, how much must you put aside each year in order to have sufficient money to retire at age 65?

32. Gordon Freeman recently invested $5,000 in a project that is promising to return 6.5 percent per year. The cash flows are expected to be as follows: End of Cash Y ear Flow 1 $1000 2 950 3 875 4 ??? 5 850 Note that the 4th year cash flow is unknown. Assuming the present value of this cash flow stream is $5,000 (that is, CF0 = -5000), what is the missing cash flow value (that is, what is the cash flow at the end of the 4th year)?

33. You have a $25,000 balance on your credit card. You plan to make monthly payments of $450 until the balance is paid off. The interest rate on your credit card is 17.5% p.a., compounded monthly. A letter in the mail informs you that you are approved for a new credit card and balance transfers are subject to a 9.5% p.a., compounded monthly. How many months sooner will you pay off your bill?

Answer 1

Based of the above given data, I calculated the entire EMI table for the required information. Anyway I used excel sheet for the EMI calculation:

Formula for calculating EMI is :- PMT(rate,nper,pv)

whereas:-

rate = rate of interest (if given in per annum then convert it into per months by dividing it with 12 months)

Nper = number of months over the payment is due or total tenure of the loan

pv = total loan amount

Formula for calculating principle payment PPMT(rate, per, nper, pv)

whereas:-

rate= rate of interest (if given in per annum then convert it into per months by dividing it with 12 months)

nper= number of months over the payment is due or total tenure of the loan

per= payment of principle of that particular month

Pv = total loan amount

So the data derived from the above given question is:-

Total Value	$208,700
Down Payment	$30,000
Loan Amount	$178,700
Rate of interest	6.25%	P.a
Tenure	84	months
EMI	2,632	by using PMT formula

EMI Table:-

Months	Payment	Principle	Interest	Beginning Balance	Ending Balance
1	$2,632.02	$1,701.29	$930.73	$178,700	$176,999
2	$2,632.02	$1,710.15	$921.87	$176,999	$175,289
3	$2,632.02	$1,719.06	$912.96	$175,289	$173,570
4	$2,632.02	$1,728.01	$904.01	$173,570	$171,841
5	$2,632.02	$1,737.01	$895.01	$171,841	$170,104
6	$2,632.02	$1,746.06	$885.96	$170,104	$168,358
7	$2,632.02	$1,755.15	$876.87	$168,358	$166,603
8	$2,632.02	$1,764.29	$867.73	$166,603	$164,839
9	$2,632.02	$1,773.48	$858.54	$164,839	$163,065
10	$2,632.02	$1,782.72	$849.30	$163,065	$161,283
11	$2,632.02	$1,792.00	$840.01	$161,283	$159,491
12	$2,632.02	$1,801.34	$830.68	$159,491	$157,689
13	$2,632.02	$1,810.72	$821.30	$157,689	$155,879
14	$2,632.02	$1,820.15	$811.87	$155,879	$154,059
15	$2,632.02	$1,829.63	$802.39	$154,059	$152,229
16	$2,632.02	$1,839.16	$792.86	$152,229	$150,390
17	$2,632.02	$1,848.74	$783.28	$150,390	$148,541
18	$2,632.02	$1,858.37	$773.65	$148,541	$146,683
19	$2,632.02	$1,868.05	$763.97	$146,683	$144,815
20	$2,632.02	$1,877.78	$754.24	$144,815	$142,937
21	$2,632.02	$1,887.56	$744.46	$142,937	$141,049
22	$2,632.02	$1,897.39	$734.63	$141,049	$139,152
23	$2,632.02	$1,907.27	$724.75	$139,152	$137,245
24	$2,632.02	$1,917.20	$714.82	$137,245	$135,327
25	$2,632.02	$1,927.19	$704.83	$135,327	$133,400
26	$2,632.02	$1,937.23	$694.79	$133,400	$131,463
27	$2,632.02	$1,947.32	$684.70	$131,463	$129,516
28	$2,632.02	$1,957.46	$674.56	$129,516	$127,558
29	$2,632.02	$1,967.65	$664.37	$127,558	$125,591
30	$2,632.02	$1,977.90	$654.12	$125,591	$123,613
31	$2,632.02	$1,988.20	$643.82	$123,613	$121,624
32	$2,632.02	$1,998.56	$633.46	$121,624	$119,626
33	$2,632.02	$2,008.97	$623.05	$119,626	$117,617
34	$2,632.02	$2,019.43	$612.59	$117,617	$115,598
35	$2,632.02	$2,029.95	$602.07	$115,598	$113,568
36	$2,632.02	$2,040.52	$591.50	$113,568	$111,527
37	$2,632.02	$2,051.15	$580.87	$111,527	$109,476
38	$2,632.02	$2,061.83	$570.19	$109,476	$107,414
39	$2,632.02	$2,072.57	$559.45	$107,414	$105,342
40	$2,632.02	$2,083.36	$548.65	$105,342	$103,258
41	$2,632.02	$2,094.22	$537.80	$103,258	$101,164
42	$2,632.02	$2,105.12	$526.90	$101,164	$99,059
43	$2,632.02	$2,116.09	$515.93	$99,059	$96,943
44	$2,632.02	$2,127.11	$504.91	$96,943	$94,816
45	$2,632.02	$2,138.19	$493.83	$94,816	$92,677
46	$2,632.02	$2,149.32	$482.69	$92,677	$90,528
47	$2,632.02	$2,160.52	$471.50	$90,528	$88,368
48	$2,632.02	$2,171.77	$460.25	$88,368	$86,196
49	$2,632.02	$2,183.08	$448.94	$86,196	$84,013
50	$2,632.02	$2,194.45	$437.57	$84,013	$81,818
51	$2,632.02	$2,205.88	$426.14	$81,818	$79,612
52	$2,632.02	$2,217.37	$414.65	$79,612	$77,395
53	$2,632.02	$2,228.92	$403.10	$77,395	$75,166
54	$2,632.02	$2,240.53	$391.49	$75,166	$72,926
55	$2,632.02	$2,252.20	$379.82	$72,926	$70,673
56	$2,632.02	$2,263.93	$368.09	$70,673	$68,409
57	$2,632.02	$2,275.72	$356.30	$68,409	$66,134
58	$2,632.02	$2,287.57	$344.45	$66,134	$63,846
59	$2,632.02	$2,299.49	$332.53	$63,846	$61,547
60	$2,632.02	$2,311.46	$320.56	$61,547	$59,235
61	$2,632.02	$2,323.50	$308.52	$59,235	$56,912
62	$2,632.02	$2,335.60	$296.42	$56,912	$54,576
63	$2,632.02	$2,347.77	$284.25	$54,576	$52,228
64	$2,632.02	$2,360.00	$272.02	$52,228	$49,868
65	$2,632.02	$2,372.29	$259.73	$49,868	$47,496
66	$2,632.02	$2,384.64	$247.38	$47,496	$45,111
67	$2,632.02	$2,397.06	$234.96	$45,111	$42,714
68	$2,632.02	$2,409.55	$222.47	$42,714	$40,305
69	$2,632.02	$2,422.10	$209.92	$40,305	$37,883
70	$2,632.02	$2,434.71	$197.31	$37,883	$35,448
71	$2,632.02	$2,447.39	$184.62	$35,448	$33,001
72	$2,632.02	$2,460.14	$171.88	$33,001	$30,540
73	$2,632.02	$2,472.95	$159.06	$30,540	$28,068
74	$2,632.02	$2,485.83	$146.18	$28,068	$25,582
75	$2,632.02	$2,498.78	$133.24	$25,582	$23,083
76	$2,632.02	$2,511.80	$120.22	$23,083	$20,571
77	$2,632.02	$2,524.88	$107.14	$20,571	$18,046
78	$2,632.02	$2,538.03	$93.99	$18,046	$15,508
79	$2,632.02	$2,551.25	$80.77	$15,508	$12,957
80	$2,632.02	$2,564.53	$67.48	$12,957	$10,392
81	$2,632.02	$2,577.89	$54.13	$10,392	$7,815
82	$2,632.02	$2,591.32	$40.70	$7,815	$5,223
83	$2,632.02	$2,604.81	$27.20	$5,223	$2,618
84	$2,632.02	$2,618.38	$13.64	$2,618	$0

29. At the end of the fourth year the balance of vito's loan will be $86,196.

30. $42,389 will be the total interest paid by vito in the entire period.

31. Following are the data derived from the above question:-

Present age	30
Investment start period	31
Investment end period	65
Total life expectancy	90
Total expenditure expected	$150,000
Rate of interest	11.25%
current deposit	$7500

By applying future value formula, we will get the total accumulate corpus by investing $7500. which will come as $2,715,668.40. This corpus will be much higher than the expected payment after retirement. by applying what if analysis, I come to the conclusion that by depositing  $3811.55 will be sufficient to get annual pension of $150,000.

Following are the table for that calculation.

Current age	Time for fund to be deposited	Amount Deposited	Present value of the annuity
31	34	$3,811.55	$142,988.89
32	33	$3,811.55	$128,529.34
33	32	$3,811.55	$115,531.99
34	31	$3,811.55	$103,848.98
35	30	$3,811.55	$93,347.40
36	29	$3,811.55	$83,907.77
37	28	$3,811.55	$75,422.72
38	27	$3,811.55	$67,795.70
39	26	$3,811.55	$60,939.96
40	25	$3,811.55	$54,777.49
41	24	$3,811.55	$49,238.19
42	23	$3,811.55	$44,259.05
43	22	$3,811.55	$39,783.41
44	21	$3,811.55	$35,760.37
45	20	$3,811.55	$32,144.16
46	19	$3,811.55	$28,893.62
47	18	$3,811.55	$25,971.80
48	17	$3,811.55	$23,345.43
49	16	$3,811.55	$20,984.66
50	15	$3,811.55	$18,862.62
51	14	$3,811.55	$16,955.16
52	13	$3,811.55	$15,240.59
53	12	$3,811.55	$13,699.41
54	11	$3,811.55	$12,314.08
55	10	$3,811.55	$11,068.83
56	9	$3,811.55	$9,949.51
57	8	$3,811.55	$8,943.38
58	7	$3,811.55	$8,039.00
59	6	$3,811.55	$7,226.06
60	5	$3,811.55	$6,495.34
61	4	$3,811.55	$5,838.51
62	3	$3,811.55	$5,248.09
63	2	$3,811.55	$4,717.39
64	1	$3,811.55	$4,240.35
65	0	$3,811.55	$3,811.55

Total Corpus accumulated is

Total Corpus

$1,380,120.78

Following is the Calculation of pension payment:-

year of pension payment	Total Corpus	Payment Taken	Corpus Remaining
	$1,380,120.78	$150,000	$1,230,120.78
1	$1,368,509.37	$150,000	$1,218,509.37
2	$1,355,591.68	$150,000	$1,205,591.68
3	$1,341,220.74	$150,000	$1,191,220.74
4	$1,325,233.07	$150,000	$1,175,233.07
5	$1,307,446.79	$150,000	$1,157,446.79
6	$1,287,659.56	$150,000	$1,137,659.56
7	$1,265,646.26	$150,000	$1,115,646.26
8	$1,241,156.46	$150,000	$1,091,156.46
9	$1,213,911.56	$150,000	$1,063,911.56
10	$1,183,601.61	$150,000	$1,033,601.61
11	$1,149,881.80	$150,000	$999,881.80
12	$1,112,368.50	$150,000	$962,368.50
13	$1,070,634.95	$150,000	$920,634.95
14	$1,024,206.39	$150,000	$874,206.39
15	$972,554.61	$150,000	$822,554.61
16	$915,092.00	$150,000	$765,092.00
17	$851,164.85	$150,000	$701,164.85
18	$780,045.89	$150,000	$630,045.89
19	$700,926.06	$150,000	$550,926.06
20	$612,905.24	$150,000	$462,905.24
21	$514,982.08	$150,000	$364,982.08
22	$406,042.56	$150,000	$256,042.56
23	$284,847.35	$150,000	$134,847.35
24	$150,017.68	$150,000	$17.68