Can someone help me on an engineering economic analysis problem?

1) Leo Messi wishes to have $20,000 at the bank at the end of 60 months. She will start saving by depositing $200 a month from today in an account that pays 6% per year, compounded monthly. She will increase her deposit by an amount $W every month until the end of the third year. At the end of the third year she will deposit $10,000 into the account. She will not touch the account for the next three years and will come back at the end of the 60th to cash her investment. What is the amount $W?

How can I solve this problem?

I believe
F = $20,000 A = $200 n = 60 and i = 6%

$W=Zero.

Look at at the chart below.


Interest Rate: 6.00%
Monthly Contribution: $200.00
SW

Month Value Contribution

1 $201.00 $200.00
2 $403.01 $200.00
3 $606.02 $200.00
4 $810.05 $200.00
5 $1,015.10 $200.00
6 $1,221.18 $200.00
7 $1,428.28 $200.00
8 $1,636.42 $200.00
9 $1,845.61 $200.00
10 $2,055.83 $200.00
11 $2,267.11 $200.00
12 $2,479.45 $200.00
13 $2,692.85 $200.00
14 $2,907.31 $200.00
15 $3,122.85 $200.00
16 $3,339.46 $200.00
17 $3,557.16 $200.00
18 $3,775.94 $200.00
19 $3,995.82 $200.00
20 $4,216.80 $200.00
21 $4,438.89 $200.00
22 $4,662.08 $200.00
23 $4,886.39 $200.00
24 $5,111.82 $200.00
25 $5,338.38 $200.00
26 $5,566.07 $200.00
27 $5,794.90 $200.00
28 $6,024.88 $200.00
29 $6,256.00 $200.00
30 $6,488.28 $200.00
31 $6,721.72 $200.00
32 $6,956.33 $200.00
33 $7,192.12 $200.00
34 $7,429.08 $200.00
35 $7,667.22 $200.00
36 $17,755.56 $10,000.00
37 $17,844.33
38 $17,933.56
39 $18,023.22
40 $18,113.34
41 $18,203.91
42 $18,294.93
43 $18,386.40
44 $18,478.33
45 $18,570.73
46 $18,663.58
47 $18,756.90
48 $18,850.68
49 $18,944.93
50 $19,039.66
51 $19,134.86
52 $19,230.53
53 $19,326.68
54 $19,423.32
55 $19,520.43
56 $19,618.04
57 $19,716.13
58 $19,814.71
59 $19,913.78
60 $20,013.35