Find n

 

This one is bugging me hard:

 

S (initial state)=10 000

 

S (base n) = 18 000

 

t = 4%

 

k= 4 

 

First equation:

 

S (base n) = S (initial state) (1+ t/k)^4n

 

SO I started here:

 

18 000 = 10 000 (1+ 0,04/4)^4n

 

Divide each side by 10 000

 

1.8 = (1+0,04/4)^4n

 

1.8 = (1.01)^4n

 

Transform this equality into a log

 

4n = log base 1.01 (1.8)

 

Put that log on base 10

 

log base 1.01 (1.8) = log (1.8) / log (1.01) = 0.25527/0.00432 = 59.09028

 

Now means

 

4n = 59.09028

 

Divide each side by 4

 

n=14.7      (was asked in the original exercice to keep only the first decimal)

 

But when I replace n with 14.7 in the original equation I end up with 10 000(1.01^58.8) wich will obviously not give 18k.

 

Halp