You deposit $5,000 into an account at the end of year 0. You deposit $5,000 every three (3) months beginning at the end of year 1 and continuing through the end of year 3. You also deposit into the account an amount X starting at the end of year 6 and repeat it every three (3) months for a total of four (4) deposits. You withdraw $112,160 at the end of year 7. After the withdrawal at the end of year 7, there is no more money in the account. The account pays 4% compounded quarterly. What is the amount you must every three (3) months deposit starting at the end of year 6 (value of X)?
Time(in years)  Deposit 
Amount with interest 

0  
0.25  
0.5  
0.75  
1  5000  
1.25  5000  5050  10050 
1.5  5000  10151  15151 
1.75  5000  15302  20302 
2  5000  20505  25505 
2.25  5000  25760  30760 
2.5  5000  31068  36068 
2.75  5000  36428  41428 
3  5000  41843  46843 
3.25  47311  47311  
3.5  47784  47784  
3.75  48262  48262  
4  48745  48745  
4.25  49232  49232  
4.5  49724  49724  
4.75  50222  50222  
5  50724  50724  
5.25  51231  51231  
5.5  51743  51743  
5.75  52261  52261  
6  52783  52783  
6.25  53311  53311  
6.5  53844  53844  
6.75  54383  54383  
7  13412  54927  68339 
7.25  13412  69022  82434 
7.5  13412  83258  96670 
7.75  13412  97637  111049 
8  112160  112160 
On solving via excel we get the value to be $13,412
**Hope this helped**
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