Partial PMT period with variable fees

[SedoSan7]

I'm trying to achieve a future goal (FV) in a known X periods of time (NPER) by investing in a project that promises 3% profit return 3% per period, however they are charging a management fee of 1% of the total FUND account or a fixed 100$ whichever is lower. With a limited Salary period, I want to do the investment in installments so I want to choose "Installments" to be the number of periods where I will pay an amount to reach that end goal of FV.

In the example provided. I use FV = $12,600, growth = 3%, Periods = 12. I used "Excel Solver" to figure out how much PMT should be for "4" installments period and the answer was $2,533.03, however I need to find this using a formula using only variables.

Partial PMT with variable PMT.xlsx
	C	D	E	F	G	H	I	J	K	L	M
6							3%	Management Charge	add	Total	Pay Out
7						0	$ -	$ -	$ 2,533.03	$ 2,533.03	$ -
8		FV	$ 12,600.00			1	$ 2,609.02	$ 26.09	$ 2,533.03	$ 5,115.95	$ -
9		Rate	3%			2	$ 5,269.43	$ 52.69	$ 2,533.03	$ 7,749.76	$ -
10	MIN of	Management Charge	$ 100.00			3	$ 7,982.26	$ 79.82	$ 2,533.03	$ 10,435.46	$ -
11		Management Charge %	1%			4	$ 10,748.53	$ 100.00	$ -	$ 10,648.53	$ -
12		period	12			5	$ 10,967.98	$ 100.00	$ -	$ 10,867.98	$ -
13		installments	4			6	$ 11,194.02	$ 100.00	$ -	$ 11,094.02	$ -
14		PMT=	$ 2,533.03			7	$ 11,426.84	$ 100.00	$ -	$ 11,326.84	$ -
15						8	$ 11,666.65	$ 100.00	$ -	$ 11,566.65	$ -
16						9	$ 11,913.65	$ 100.00	$ -	$ 11,813.65	$ -
17		Only values allowed to change to test result				10	$ 12,168.06	$ 100.00	$ -	$ 12,068.06	$ -
18		Should be equal				11	$ 12,430.10	$ 100.00	$ -	$ 12,330.10	$ -
19		Find fully functional function with NO static values				12	$ 12,700.00	$ 100.00	$ -	$ 12,600.00	$ 12,600.00
20						13	$ 0.00	$ -	$ -	$ 0.00	$ -
21		Condition		Status		14	$ 0.00	$ -	$ -	$ 0.00	$ -
22		Management charge contains 100		Pass		15	$ 0.00	$ -	$ -	$ 0.00	$ -
23		Management charge contains between 0 100		Pass		16	$ 0.00	$ -	$ -	$ 0.00	$ -
24		Found FV		Pass		17	$ 0.00	$ -	$ -	$ 0.00	$ -
25						18	$ 0.00	$ -	$ -	$ 0.00	$ -
26						19	$ 0.00	$ -	$ -	$ 0.00	$ -
27						20	$ 0.00	$ -	$ -	$ 0.00	$ -
28						21	$ 0.00	$ -	$ -	$ 0.00	$ -
29						22	$ 0.00	$ -	$ -	$ 0.00	$ -
30						23	$ 0.00	$ -	$ -	$ 0.00	$ -
31						24	$ 0.00	$ -	$ -	$ 0.00	$ -
Sheet16

Cell Formulas
Range	Formula
I6	I6	=$E$9
K7:K31	K7	=IF($E$13>H7,$E$14,0)
L7:L31	L7	=I7-J7+K7
M7:M31	M7	=IF(H7=$E$12,$E$8,0)
I8:I31	I8	=(L7-M7)*(1+$E$9)
J8:J31	J8	=IF($E$12>=H8,MIN(I8*$E$11,$E$10),0)
D22	D22	="Management charge contains "&$E$10
D23	D23	="Management charge contains between 0 "&$E$10
F22	F22	=IF(COUNTIF($J$7:$J$31,$E$10)>0,"Pass","Fail")
F23	F23	=IF(COUNTIFS($J$7:$J$31,">"&0,$J$7:$J$31,"<"&$E$10)>0,"Pass","Fail")
F24	F24	=IF($E$8=VLOOKUP($E$12,$H$7:$L$31,5,FALSE),"Pass","Fail")

Cells with Conditional Formatting
Cell	Condition		Cell Format	Stop If True
F22:F24	Cell Value	="Fail"	text	NO
E14:F14	Expression	=$E$8<>$L$19	text	NO
L7:L31	Expression	=AND($H7=$E$12,$L7=$E$8)	text	NO

Cells with Data Validation
Cell	Allow	Criteria
E12	Whole number	between 1 and 24
E13	Whole number	between 1 and $E$12