# Exponential growth and compound interest

• alexandria
In summary, the conversation was about using the "rule of 72" to estimate the number of years it takes for an investment to double. The equation A = P(1+i)^n was discussed, with P representing the initial investment, i representing the annual percentage rate, and n representing the number of years. The attempt at a solution was verified to be correct, and the "rule of 72" was considered a useful rule of thumb for financial calculations.

A = P(1+i)^n

## The Attempt at a Solution

Here is my attempted solution, can someone please verify if my method is correct!
Thanks in advance![/B]

alexandria said:

## Homework Statement

View attachment 101167

A = P(1+i)^n

## The Attempt at a Solution

Here is my attempted solution, can someone please verify if my method is correct!
Thanks in advance![/B]
View attachment 101166

It looks OK.

This is a good example of the "rule of 72", which is a rule of thumb used by financial people. Basically it says that the number of years it takes for an investment to double is equal to 72 divided by the annual percentage rate. In this case 72/4 = 18, quite close to your more exact solution.

ok thanks for the help!

## What is exponential growth?

Exponential growth is a type of growth in which the value of a quantity increases at an increasing rate over time. This means that the amount by which the quantity grows also increases over time.

## How does exponential growth differ from linear growth?

In linear growth, the value of a quantity increases by a fixed amount over a certain period of time. In exponential growth, the value of a quantity increases by a fixed percentage over a certain period of time.

## What is compound interest?

Compound interest is a type of interest calculation in which the interest earned is added to the principal amount, and then the interest is calculated again on the new total. This results in exponential growth of the initial investment.

## How does compound interest impact savings and investments?

Compound interest can significantly increase the value of savings and investments over time. The longer the time period and the higher the interest rate, the greater the impact of compound interest.

## What factors affect the rate of exponential growth and compound interest?

The rate of exponential growth and compound interest is affected by the initial amount invested, the interest rate, the compounding frequency, and the time period. Higher initial amounts, interest rates, and compounding frequencies will result in a faster rate of growth. A longer time period will also result in a higher total amount earned through compound interest.