2=16^(1/4)?

Question

I'm making a small table in Excel to calculate the increase between 2 levels in different ways. There's one that I can't get solved. I think it's a mathematical problem, but I can't find out what's wrong with it.
It's about the number of steps it takes for something to increase to another level if the increase per step is constant.

Example:
Start = 5,000
End = 25,272
% = Inrease per step = 10% = 0.1

Number of steps = (Start / End) ^ (1 / (1 + %)) <-- (I think the error is in here)
= 5.054 ^ 0.909
= 4.36

In Excel:
A1 = Start: 5,000
B1 = End : 25,272
D1 = % increase per step: 10% = 0.1
C1 = number of steps = (B1/A1)^(1/(1+D1))

The problem is that the answer should be 17.

What should the right formula be to solve the problem?

Haha Triplefull, I saw that ;-)
I may not vote for a few hours yet, so I'll have to wait for that, but it seems the problem is solved. It's been years ago since I learned about LN's and log and stuff like that, and never used it since, so I don't know what I'm doing, but it works.
Thanks people.

Answer 1

Hello there,

Actually you should do : C1 = LN(End/Start)/LN(1+%)

Let me explain:
Your problem is to find the number of period n in
End = Start (1+rate)^n
so:
end/start=(1+rate)^n
then:
ln(end/start)=ln((1+rate)^n)
which leads to:
ln(end/start)=n * ln (1+rate)

As a result:
n= ln(end/start)/ln(1+rate)


So you should do:

C1 = LN(End/Start)/LN(1+%)

and you'll find 17.

Answer 2

a1 = 5000 -- start point, entered manually
b1 = 25272 -- end point, entered manually
c1 = (B1/A1)^(1/D1)-1
d1 = # of steps -- entered manually

This will allow you to find out the percent increase needed per step to achieve your result. It assumes that you know the number of steps and can enter that manually.

Your questions seems to suggest you want to enter the percent increase and find the # of steps.... Therefore, the set up would look like this....

a1 = 5000 -- start point, entered manually
b1 = 25272 -- end point, entered manually
c1 = % increase -- entered manually (in your example = .1)
d1 = LN(B1/A1)/LN(1+C1)

The answer in D1 will actually be 16.99985 which isn't 17, but awfully darn close!

Answer 3

You've got the right idea in that 10% should be written 0.1, 5% written 0.05, etc. Call this decimal "d". Then, if x = number of steps:

(1+d)^x = 5.0544 (end value divided by start value)

Take logs:

x*log(1+d) = log 5.0544

Rearrange:

x = log 5.0544 / log(1+d)

Using your example, x = log 5.0544 / log 1.1
= 0.7037 / 0.0414
=16.998 [17 if done more accurately using a computer]

Hope you can now set up a spreadsheet.

Answer 4

Your formula is not in order ~ you have to adopt the compounding formula ie., Sum = P (1+ R/100)^n
here you got all the factors excepting ~ n
Sum = 25,272
P = 5,000
R = 10
n = ? (we should arrive at)
by substituting the numbers -
25,272 = 5000(1+10/100)^n
25272/5000 = (1.10)^n
5.0544 = (1.10)^17

Hope U have the solution.

Answer 5

your problem is not clear