Question

a. Steve and Jackson have $4,000 to deposit in a money market fund earning 5%. If they add $2,000 to that account annually, how much will they have accumulated in 15 years? (Show all work.)

b. Carey has $2,000 for a down payment on a vehicle and she can afford monthly payments of $400. She wants to finance a vehicle over no more than 4 years. If lenders are currently offering loans at 6 percent interest, what is the maximum price Judy can pay for a vehicle?

c. Pat would like to know the monthly payments and the total finance charges on the following 2 loans: (Show all work.)

A.. $30,000, 9%, 36 months
B. $30,000, 9%, 48 months

d. Your mortgage payment is $1,500 per month. Of this amount, insurance is $50, property taxes are $200, and interest is about $1,100. Assuming you have other itemized deductions that already exceed your standard deduction and that you are in the 31% marginal tax bracket, what is the reduction in your tax liability as a result of owning a home with this mortgage. (Show all work.)

Answer 1

(A)

Time	Additions made to the account	Value at the end of 15 Years (5% p.a. compounding)
0	4000	8316
1	2000	3960
2	2000	3771
3	2000	3592
4	2000	3421
5	2000	3258
6	2000	3103
7	2000	2955
8	2000	2814
9	2000	2680
10	2000	2553
11	2000	2431
12	2000	2315
13	2000	2205
14	2000	2100
15	2000	2000

Hence, accumulated value (at the end of the 15 years) = $ 51,473

(B)

Number of Months	Compounding monthly at = 6%/12
48	508
47	506
46	503
45	501
44	498
43	496
42	493
41	491
40	488
39	486
38	483
37	481
36	479
35	476
34	474
33	472
32	469
31	467
30	465
29	462
28	460
27	458
26	455
25	453
24	451
23	449
22	446
21	444
20	442
19	440
18	438
17	435
16	433
15	431
14	429
13	427
12	425
11	423
10	420
9	418
8	416
7	414
6	412
5	410
4	408
3	406
2	404
1	402

To understand the calculations, she pays either an EMI or she deposits in an account that pays monthly compounding interest rate of 6%/12 = 0.5%.

The above cash flows tell us what each of her monthly contributions amount to at the end of 4 years (48 months). When we sum all these up, we get a value of $ 21,747 as on 4 years from today. Calculating the Present Value of this amount (at 6%/12 monthly compounding), we get = $ 5,263.

Hence, the maximum price she can pay for a vehicle = Loan amount + Down Payment = $ 7,263

(C) Using MSExcel, = PMT (9%/12, 36, 30000), we get EMI of $ 954.

Using MSExcel = PMT(9%/12, 48, 30000), we get EMI of $ 747

Month Number	EMI Amount	Interest Amount	Principal Amount	Cumulative Principal Paid	Outstanding Principal
1	954	225	729	729	29271
2	954	220	734	1463	28537
3	954	214	740	2203	27797
4	954	208	746	2949	27051
5	954	203	751	3700	26300
6	954	197	757	4457	25543
7	954	192	762	5219	24781
8	954	186	768	5987	24013
9	954	180	774	6761	23239
10	954	174	780	7541	22459
11	954	168	786	8326	21674
12	954	163	791	9118	20882
13	954	157	797	9915	20085
14	954	151	803	10719	19281
15	954	145	809	11528	18472
16	954	139	815	12343	17657
17	954	132	822	13165	16835
18	954	126	828	13993	16007
19	954	120	834	14827	15173
20	954	114	840	15667	14333
21	954	107	846	16513	13487
22	954	101	853	17366	12634
23	954	95	859	18226	11774
24	954	88	866	19091	10909
25	954	82	872	19963	10037
26	954	75	879	20842	9158
27	954	69	885	21727	8273
28	954	62	892	22619	7381
29	954	55	899	23518	6482
30	954	49	905	24423	5577
31	954	42	912	25336	4664
32	954	35	919	26255	3745
33	954	28	926	27180	2820
34	954	21	933	28113	1887
35	954	14	940	29053	947
36	954	7	947	30000	0

Cumulative Interest Paid = $ 4,344 on the 9%, 36 Months loan

Month Number	EMI Amount	Interest Amount	Principal Amount	Cumulative Principal Paid	Outstanding Principal
1	747	225	522	522	29478
2	747	221	525	1047	28953
3	747	217	529	1576	28424
4	747	213	533	2110	27890
5	747	209	537	2647	27353
6	747	205	541	3189	26811
7	747	201	545	3734	26266
8	747	197	550	4284	25716
9	747	193	554	4837	25163
10	747	189	558	5395	24605
11	747	185	562	5957	24043
12	747	180	566	6523	23477
13	747	176	570	7094	22906
14	747	172	575	7669	22331
15	747	167	579	8248	21752
16	747	163	583	8831	21169
17	747	159	588	9419	20581
18	747	154	592	10011	19989
19	747	150	597	10608	19392
20	747	145	601	11209	18791
21	747	141	606	11814	18186
22	747	136	610	12425	17575
23	747	132	615	13039	16961
24	747	127	619	13659	16341
25	747	123	624	14283	15717
26	747	118	629	14911	15089
27	747	113	633	15545	14455
28	747	108	638	16183	13817
29	747	104	643	16826	13174
30	747	99	648	17473	12527
31	747	94	653	18126	11874
32	747	89	657	18784	11216
33	747	84	662	19446	10554
34	747	79	667	20113	9887
35	747	74	672	20786	9214
36	747	69	677	21463	8537
37	747	64	683	22146	7854
38	747	59	688	22833	7167
39	747	54	693	23526	6474
40	747	49	698	24224	5776
41	747	43	703	24927	5073
42	747	38	709	25636	4364
43	747	33	714	26350	3650
44	747	27	719	27069	2931
45	747	22	725	27794	2206
46	747	17	730	28524	1476
47	747	11	735	29259	741
48	747	6	741	30000	0

Cumulative Interest Payment = $ 5,834

(D) Because of owning the home, the interest payments give income tax rebates. Hence, the monthly reduction in tax liabilities because of interest payments = 31% x $1,100 = $ 341.