# How Many Times Do I Have To Increase by 3%?

• MHB
• piAreRound1
Also, that formula only applies for continuous compounding, while the problem at hand deals with discrete compounding. The formula I provided in the conversation takes that into account and provides the correct solution.
piAreRound1
I want to know how many time I have to increase 30 by 3% before it is greater or equal to 500.

I think this is the correct formula:
30 * 1.03^x >= 500

What steps do I have to take to solve it?

I would write:

$$\displaystyle 30\cdot1.03^n\ge500$$

Divide through by 30:

$$\displaystyle 1.03^n\ge\frac{50}{3}$$

Take the natural log of both sides, and apply a log rule to obtain:

$$\displaystyle n\ln(1.03)\ge\ln\left(\frac{50}{3}\right)$$

Hence:

$$\displaystyle n\ge\frac{\ln\left(\dfrac{50}{3}\right)}{\ln(1.03)}$$

Since presumably $$n$$ is an integer, we could write:

$$\displaystyle n=\left\lceil\frac{\ln\left(\dfrac{50}{3}\right)}{\ln(1.03)}\right\rceil$$

This is the "ceiling" function and it tells us to round up to the nearest integer. According to W|A, we find:

$$\displaystyle n=96$$

Wolfram|Alpha: Computational Intelligence

piAreRound said:
I want to know how many time I have to increase 30 by 3% before it is greater or equal to 500.

if a^p = b then p = ln(b) / ln(a)

My wrist is getting awfully crowded!

## 1. How do I calculate the number of times I need to increase by 3%?

To calculate the number of times you need to increase by 3%, you can use the following formula: number of times = log(final value / initial value) / log(1.03). This formula is based on the compound interest formula, where 1.03 represents the growth rate of 3%.

## 2. What is the significance of increasing by 3%?

Increasing by 3% is significant because it represents a steady growth rate over time. It is commonly used in financial planning and investments to calculate potential earnings or returns.

## 3. How does increasing by 3% compare to other growth rates?

Increasing by 3% is considered a moderate growth rate. It is higher than the average inflation rate, which is around 2%, but lower than the average stock market return, which is around 7%. However, the significance of a growth rate depends on the context and the specific situation.

## 4. Can I use the 3% increase rule for any type of value?

The 3% increase rule can be applied to any type of value as long as it is a consistent growth rate. However, it is important to note that in some cases, a different growth rate may be more appropriate, such as for rapidly growing values or those affected by compounding.

## 5. What are the limitations of using the 3% increase rule?

The 3% increase rule is based on the assumption of a constant growth rate, which may not always hold true. It also does not take into account external factors that may affect the growth of a value. Additionally, it is important to regularly reassess and adjust the growth rate as needed to accurately reflect the changing circumstances.

• General Math
Replies
4
Views
1K
• General Math
Replies
4
Views
2K
• General Math
Replies
14
Views
2K
• General Math
Replies
3
Views
1K
• Cosmology
Replies
12
Views
935
• General Math
Replies
1
Views
1K
• General Math
Replies
1
Views
1K
• General Math
Replies
2
Views
10K
• General Math
Replies
5
Views
1K
• General Math
Replies
6
Views
2K