if i have 25547 and add 1410 to that sum i get = 26957. if i reduce that new sum with 5 % i get = 25609,15. if i repeat this process each da

You can get 28200 if u dont reduce it with 5 % the last day.

You get max 20 * 1410 = 28200.

$$\small{\text{$ \boxed{~~t_n=0.95^n\cdot \left( \dfrac{25547}{0.95}-20\cdot 1410 \right)+20\cdot 1410~~} $}}\\\\ \small{\text{We have $t_n = 27924$ and get n by rearrange: }}\\\\ \small{\text{$ \boxed{ n=\dfrac {\ln{\left( \dfrac{t_n -20\cdot 1410}{ \dfrac{25547}{0.95} -20\cdot 1410} \right)}} {\ln{(0.95)}} } $}}\\\\\\ \small{\text{$ \begin{array}{rcl} n &=& \dfrac {\ln{\left( \dfrac{27924 -20\cdot 1410}{\dfrac{25547}{0.95}-20\cdot 1410} \right)}} {\ln{(0.95)}}\\\\ n &=& \dfrac {\ln{\left( \dfrac{-276}{ -1308.42105263} \right)}} {\ln{(0.95)}}\\\\ n &=& \dfrac {\ln{\left( 0.21094127112\right)}} {\ln{(0.95)}}\\\\ n &=& \dfrac {-1.55617552018} {-0.05129329439}\\\\ \mathbf{n} & \mathbf{=} & \mathbf{30.3387711544} \end{array} $}}$$

It will take to get 27924 about 30.3387711544 days

day 30 = 27919.16 

day 31 = 27933.20


$$\small{\text{$ 
 \begin{array}{lr}
 \small{\text{day }} 1 & 26957.00 \\
 \small{\text{day }} 2 & 27019.15 \\
 \small{\text{day }} 3 & 27078.19 \\
 \small{\text{day }} 4 & 27134.28 \\
 \small{\text{day }} 5 & 27187.57 \\
 \small{\text{day }} 6 & 27238.19 \\
 \small{\text{day }} 7 & 27286.28 \\
 \small{\text{day }} 8 & 27331.97 \\ 
 \small{\text{day }} 9 & 27375.37 \\
 \small{\text{day }} 10 & 27416.60 \\
 \small{\text{day }} 11 & 27455.77 \\
 \small{\text{day }} 12 & 27492.98 \\
 \small{\text{day }} 13 & 27528.33 \\
 \small{\text{day }} 14 & 27561.92 \\
 \small{\text{day }} 15 & 27593.82 \\
 \small{\text{day }} 16 & 27624.13 \\
 \small{\text{day }} 17 & 27652.92 \\
 \small{\text{day }} 18 & 27680.28 \\
 \small{\text{day }} 19 & 27706.26 \\
 \small{\text{day }} 20 & 27730.95 \\
 \small{\text{day }} 21 & 27754.40 \\
 \small{\text{day }} 22 & 27776.68 \\
 \small{\text{day }} 23 & 27797.85 \\
 \small{\text{day }} 24 & 27817.96 \\
 \small{\text{day }} 25 & 27837.06 \\
 \small{\text{day }} 26 & 27855.20 \\
 \small{\text{day }} 27 & 27872.44 \\
 \small{\text{day }} 28 & 27888.82 \\
 \small{\text{day }} 29 & 27904.38 \\
 \small{\text{day }} 30 & 27919.16 \\
 \small{\text{day }} 31 & 27933.20
 \end{array}
 $}}$$

if i have 25547 and add 1410 to that sum i get = 26957. if i reduce that new sum with 5 % i get = 25609,15. if i repeat this process each day, how many days will it take to get to 27924?

If I have properly understood: You get max 19 * 1410 = 26790

(19 = 0.95/0.05)

You never reach 27924!

I should have clarifyed.

You can get 28200 if u dont reduce it with 5 % the last day.

So how many days will it take to reach 27924 if u start at 25547, add 1410 each day and reduse that new totalsum with 5%?

On the day u reach 27924 u dont reduce the sum.

Thank you so much:)

Thanks Heureka :)   

I'm confused but hopefully a little concentrated effort (of my own) will sort me out .