Exponential growth and compound interest

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SUMMARY

The discussion centers on the application of the formula A = P(1+i)^n to calculate compound interest and the concept of exponential growth in investments. Participants confirm the validity of the method presented and reference the "rule of 72," a financial heuristic that estimates the time required for an investment to double by dividing 72 by the annual interest rate. In this case, an annual percentage rate of 4% results in an approximate doubling time of 18 years, aligning closely with the calculated outcome.

PREREQUISITES
  • Understanding of compound interest and the formula A = P(1+i)^n
  • Familiarity with the "rule of 72" for estimating investment growth
  • Basic knowledge of financial mathematics
  • Ability to perform percentage calculations
NEXT STEPS
  • Research the derivation and applications of the compound interest formula A = P(1+i)^n
  • Explore the "rule of 72" and its limitations in financial forecasting
  • Learn about different types of interest rates, including simple and compound interest
  • Investigate advanced financial modeling techniques for investment growth analysis
USEFUL FOR

Students studying finance, educators teaching financial mathematics, and individuals interested in personal investment strategies.

alexandria
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Homework Statement


upload_2016-5-23_19-58-57.png


Homework Equations


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]
upload_2016-5-23_19-58-38.png
 
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alexandria said:

Homework Statement


View attachment 101167

Homework Equations


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!
 

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