Question

0. Winston deposits $A in an account today. He plans to withdraw $200 at the beginning of every year for 15 years, first withdrawal today. The account earns j2 = 6% for the first 8 years and j2 = 4% thereafter. What is the value of A?

   b) Deposits of $300 are made at the end of each month for five years into an account that earns interest at j2 = 5%. The account credits simple interest for fractional periods. What is the accumulated value of this account just after the 60th monthly deposit is made?

Answer 1

Part A:

= CF * [ ( PVAF @6%, 8) + PVAF ( 4%, 9 to 15) ]

= $ 200 * [ 6.5823 + 3.9917 ]

= $ 200 * 10.5741

= $ 2114.82

Value Today = PV of CFs received

Year	CF	PVF	Disc CF
1	$ 200.00	1.0000	$    200.00
2	$ 200.00	0.9434	$    188.68
3	$ 200.00	0.8900	$    178.00
4	$ 200.00	0.8396	$    167.92
5	$ 200.00	0.7921	$    158.42
6	$ 200.00	0.7473	$    149.45
7	$ 200.00	0.7050	$    140.99
8	$ 200.00	0.6651	$    133.01
9	$ 200.00	0.6395	$    127.90
10	$ 200.00	0.6149	$    122.98
11	$ 200.00	0.5912	$    118.25
12	$ 200.00	0.5685	$    113.70
13	$ 200.00	0.5466	$    109.33
14	$ 200.00	0.5256	$    105.12
15	$ 200.00	0.5054	$    101.08
Value Today	$2,114.82

Part B:

Month	Dep	Int	Total
1	$ 300.00	$   73.75	$      373.75
2	$ 300.00	$   72.50	$      372.50
3	$ 300.00	$   71.25	$      371.25
4	$ 300.00	$   70.00	$      370.00
5	$ 300.00	$   68.75	$      368.75
6	$ 300.00	$   67.50	$      367.50
7	$ 300.00	$   66.25	$      366.25
8	$ 300.00	$   65.00	$      365.00
9	$ 300.00	$   63.75	$      363.75
10	$ 300.00	$   62.50	$      362.50
11	$ 300.00	$   61.25	$      361.25
12	$ 300.00	$   60.00	$      360.00
13	$ 300.00	$   58.75	$      358.75
14	$ 300.00	$   57.50	$      357.50
15	$ 300.00	$   56.25	$      356.25
16	$ 300.00	$   55.00	$      355.00
17	$ 300.00	$   53.75	$      353.75
18	$ 300.00	$   52.50	$      352.50
19	$ 300.00	$   51.25	$      351.25
20	$ 300.00	$   50.00	$      350.00
21	$ 300.00	$   48.75	$      348.75
22	$ 300.00	$   47.50	$      347.50
23	$ 300.00	$   46.25	$      346.25
24	$ 300.00	$   45.00	$      345.00
25	$ 300.00	$   43.75	$      343.75
26	$ 300.00	$   42.50	$      342.50
27	$ 300.00	$   41.25	$      341.25
28	$ 300.00	$   40.00	$      340.00
29	$ 300.00	$   38.75	$      338.75
30	$ 300.00	$   37.50	$      337.50
31	$ 300.00	$   36.25	$      336.25
32	$ 300.00	$   35.00	$      335.00
33	$ 300.00	$   33.75	$      333.75
34	$ 300.00	$   32.50	$      332.50
35	$ 300.00	$   31.25	$      331.25
36	$ 300.00	$   30.00	$      330.00
37	$ 300.00	$   28.75	$      328.75
38	$ 300.00	$   27.50	$      327.50
39	$ 300.00	$   26.25	$      326.25
40	$ 300.00	$   25.00	$      325.00
41	$ 300.00	$   23.75	$      323.75
42	$ 300.00	$   22.50	$      322.50
43	$ 300.00	$   21.25	$      321.25
44	$ 300.00	$   20.00	$      320.00
45	$ 300.00	$   18.75	$      318.75
46	$ 300.00	$   17.50	$      317.50
47	$ 300.00	$   16.25	$      316.25
48	$ 300.00	$   15.00	$      315.00
49	$ 300.00	$   13.75	$      313.75
50	$ 300.00	$   12.50	$      312.50
51	$ 300.00	$   11.25	$      311.25
52	$ 300.00	$   10.00	$      310.00
53	$ 300.00	$      8.75	$      308.75
54	$ 300.00	$      7.50	$      307.50
55	$ 300.00	$      6.25	$      306.25
56	$ 300.00	$      5.00	$      305.00
57	$ 300.00	$      3.75	$      303.75
58	$ 300.00	$      2.50	$      302.50
59	$ 300.00	$      1.25	$      301.25
60	$ 300.00	$          -	$      300.00
After after 60 Months	$ 20,212.50

Int = Deposit * (5%/12) * No. of Months balance