If I was smarter I'd know how to ask this better

mbyington · **Joined:** Tue, 6 Mar 2012 22:01:36 UTC **Posts:** 4

If I want to know how many times I add a fixed percentage to a number before I reach a target, how would I go about doing that.

For example, if I start with 100 I need to add 1% x number of times before reaching 150. Using an excel spreadsheet I figure out it was 40 times but there must be a better way.

If you could also enlighten me with the correct phrasing for this question, I'd appreciate it.

Thanks!

Shadow · **Posted:** Tue, 6 Mar 2012 22:13:53 UTC

mbyington wrote:

If I want to know how many times I add a fixed percentage to a number before I reach a target, how would I go about doing that.

For example, if I start with 100 I need to add 1% x number of times before reaching 150. Using an excel spreadsheet I figure out it was 40 times but there must be a better way.

If you could also enlighten me with the correct phrasing for this question, I'd appreciate it.

Thanks!

Do you mean repeatedly add 1% of whatever you have at the time or 1% of the original amount?

In the first case, let x be your original amount, then 1% of x is 0.01x

, so add that to x and you get the new number x_1=x+0.01x=1.01x

. Then define x_n=(1.01)^nx

which iteratively does the same thing each time. Let your target be a fixed number,

, then to solve for

, the formula is x(1.01)^n=T

, so you get: $n={1\over \log(1.01)}\log{T\over x}$ .

If you're adding 0.01x each time instead of 0.01 of whatever you have, then it's even easier, the formula is x+n*(0.01)x=T

then $n={T-x\over 0.01x}=100{T-x\over x}=100({T\over x}-1)$ .

mbyington · **Joined:** Tue, 6 Mar 2012 22:01:36 UTC **Posts:** 4

To clarify, I want to keep adding 1% to the product every time, thus the 1% is a steadily growing amount.

What is that strange cursive-looking little uppercase I ?

For dummies here... could you walk me through this equation going from 100 to 150 by increasing 1% using a calculator?

Thank you so much, by the way.

Shadow · **Posted:** Tue, 6 Mar 2012 22:31:53 UTC

mbyington wrote:

To clarify, I want to keep adding 1% to the product every time, thus the 1% is a steadily growing amount.

What is that strange cursive-looking little uppercase I ?

For dummies here... could you walk me through this equation going from 100 to 150 by increasing 1% using a calculator?

Thank you so much, by the way.

I'm not sure what you mean by little upper-case l. Do you mean the letter I or the letter L (both are currently upper-case). And which line is it on/what is it next to?

The formula you need is the first one I gave you in the case you describe.

Shadow · **Posted:** Tue, 6 Mar 2012 22:35:19 UTC

Also, topic moved to Algebra.

Shadow · **Posted:** Tue, 6 Mar 2012 22:36:48 UTC

mbyington wrote:

To clarify, I want to keep adding 1% to the product every time, thus the 1% is a steadily growing amount.

What is that strange cursive-looking little uppercase I ?

For dummies here... could you walk me through this equation going from 100 to 150 by increasing 1% using a calculator?

Thank you so much, by the way.

I don't know what you mean by "using a caculator", the method doesn't use a calculator to figure out the formula, and if you want to actually solve for n it is as simple as plugging in the formula to a calculator, so I cannot say much more than "press the right keys so that the formula I posted is what is calculated".

mbyington · **Joined:** Tue, 6 Mar 2012 22:01:36 UTC **Posts:** 4

What's this after the 0.01?

Shadow · **Posted:** Tue, 6 Mar 2012 22:41:52 UTC

mbyington wrote:

What's this after the 0.01?

It's the letter x, which I said should denote how much you started with. You'll have to excuse how the math font is rendered, that's just how it displays "x".

mbyington · **Joined:** Tue, 6 Mar 2012 22:01:36 UTC **Posts:** 4

thank you, Shadow. I appreciate it very much.

(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Shadow · **Posted:** Tue, 6 Mar 2012 22:47:38 UTC

mbyington wrote:

thank you, Shadow. I appreciate it very much.

(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Glad to help.

BTW, if you want to add bunny to your signature, just head over to your profile and copy it there, and you'll find you don't have to put it on every post manually. ^_^

Denis · **Posted:** Wed, 7 Mar 2012 02:24:45 UTC

mbyington wrote:

For example, if I start with 100 I need to add 1% x number of times before reaching 150.

That's the same as depositing $100 in an account paying 1% monthly:
how many months does it take to accumulate to $150 ?

Formula: F = A(1 + i)^n
F = Future value (150)
A = Present value (100)
i = interest rate (.01)
n = number of months (?)

In terms of n, formula becomes: n = LOG(F/A) / LOG(1 + i)

So n = LOG(150/100) / LOG(1.01) = 40.7489 or "not quite 41 months"...

Shadow · **Posted:** Wed, 7 Mar 2012 02:27:17 UTC

Denis wrote:

mbyington wrote:

For example, if I start with 100 I need to add 1% x number of times before reaching 150.

That's the same as depositing $100 in an account paying 1% monthly:
how many months does it take to accumulate to $150 ?

Formula: F = A(1 + i)^n
F = Future value (150)
A = Present value (100)
i = interest rate (.01)
n = number of months (?)

In terms of n, formula becomes: n = LOG(F/A) / LOG(1 + i)

So n = LOG(150/100) / LOG(1.01) = 40.7489 or "not quite 41 months"...

Which is exactly what I said.

Denis · **Posted:** Wed, 7 Mar 2012 02:34:06 UTC

Shadow wrote:

Which is exactly what I said.

Agree. Was trying to show in "another language/style" ! :idea:

S.O.S. Mathematics CyberBoard

If I was smarter I'd know how to ask this better

Who is online