Systems of Equations
Adding and Subtracting Rational Expressions with Different Denominators
Graphing Linear Equations
Raising an Exponential Expression to a Power
Horizontal Line Test
Quadratic Equations
Mixed Numbers and Improper Fractions
Solving Quadratic Equations by Completing the Square
Solving Exponential Equations
Adding and Subtracting Polynomials
Factorizing simple expressions
Identifying Prime and Composite Numbers
Solving Linear Systems of Equations by Graphing
Complex Conjugates
Graphing Compound Inequalities
Simplified Form of a Square Root
Solving Quadratic Equations Using the Square Root Property
Multiplication Property of Radicals
Determining if a Function has an Inverse
Scientific Notation
Degree of a Polynomial
Factoring Polynomials by Grouping
Solving Linear Systems of Equations
Exponential Functions
Factoring Trinomials by Grouping
The Slope of a Line
Simplifying Complex Fractions That Contain Addition or Subtraction
Solving Absolute Value Equations
Solving Right Triangles
Solving Rational Inequalities with a Sign Graph
Domain and Range of a Function
Multiplying Polynomials
Slope of a Line
Multiplying Rational Expressions
Percent of Change
Equations Involving Fractions or Decimals
Simplifying Expressions Containing only Monomials
Solving Inequalities
Quadratic Equations with Imaginary Solutions
Reducing Fractions to Lowest Terms
Prime and Composite Numbers
Dividing with Exponents
Dividing Rational Expressions
Equivalent Fractions
Graphing Quadratic Functions
Linear Equations and Inequalities in One Variable
Notes on the Difference of 2 Squares
Solving Absolute Value Inequalities
Solving Quadratic Equations
Factoring Polynomials Completely
Using Slopes to Graph Lines
Fractions, Decimals and Percents
Solving Systems of Equations by Substitution
Quotient Rule for Radicals
Prime Polynomials
Solving Nonlinear Equations by Substitution
Simplifying Radical Expressions Containing One Term
Factoring a Sum or Difference of Two Cubes
Finding the Least Common Denominator of Rational Expressions
Multiplying Rational Expressions
Expansion of a Product of Binomials
Solving Equations
Exponential Growth
Factoring by Grouping
Solving One-Step Equations Using Models
Solving Quadratic Equations by Factoring
Adding and Subtracting Polynomials
Rationalizing the Denominator
Rounding Off
The Distributive Property
What is a Quadratic Equation
Laws of Exponents and Multiplying Monomials
The Slope of a Line
Factoring Trinomials by Grouping
Multiplying and Dividing Rational Expressions
Solving Linear Inequalities
Multiplication Property of Exponents
Multiplying and Dividing Fractions 3
Dividing Monomials
Multiplying Polynomials
Adding and Subtracting Functions
Dividing Polynomials
Absolute Value and Distance
Multiplication and Division with Mixed Numbers
Factoring a Polynomial by Finding the GCF
Adding and Subtracting Polynomials
The Rectangular Coordinate System
Polar Form of a Complex Number
Exponents and Order of Operations
Graphing Horizontal and Vertical Lines
Invariants Under Rotation
The Addition Method
Solving Linear Inequalities in One Variable
The Pythagorean Theorem
Try the Free Math Solver or Scroll down to Tutorials!












Please use this form if you would like
to have this math solver on your website,
free of charge.

Exponential Growth: Compound Interest

An example of an exponential growth function is compound interest. Compound interest means that the interest you earn after a certain period of time is added to your initial investment. Then, you earn interest on your initial investment and on the interest that you have earned. That is, your interest compounds.

The following formula can be used to calculate compound interest.


Formula — Compound Interest With n Compounding Periods

The amount of money in an account that earns compound interest is given by the following formula:


A = amount in the account after t years.

P = principal (amount on which the interest is calculated).

r = annual percentage rate, written in decimal form.

n = number of times the interest is compounded per year.

t = number of years the money is invested.


Example 1

Wendy invested $1000 in an account that earns 6% interest per year.

a. Find the amount, A, after 5 years if the interest is compounded quarterly.

b. Use the graph to approximate the number of years it will take for the investment to be worth $2000.


a. Use the compound interest formula.

Amount invested, P = 1000.

Interest rate, r = 6% = 0.06.

Number of times compounded per year, n = 4

Number of years invested, t = 5.

  Substitute the values for the variables.
  Simplify inside the parentheses.

Simplify the exponent.

Use a calculator to find (1.015)20.

Leave the result on your calculator until you multiply by 1000. This will minimize the rounding error. Multiply and round to the nearest cent.

Multiply and round to the nearest cent.

A = 1000(1.015)4 · 5

A = 1000(1.015) 20



A ≈ 1000 (1.346855007)

A ≈ $ 1346.86

  So, after 5 years Wendy will have approximately $1346.86.

We can use the graph to check that $ 1346.86 is a reasonable solution.

• First, find t = 5 on the t-axis.

• Then, move vertically until you intersect the graph.

• Then move left to the A-axis.

• Finally read the value.

The value appears to be about $ 1400. So, our calculation of $1346.86 is reasonable.

b. On the graph, find 2000 on the A-axis. Then, move horizontally until you intersect the graph, move down to the t-axis, and finally read the value. It appears to be slightly less than 12, say 11.6.

So, the amount in the account will grow to $2000 in about 11.6 years.


To find 1.01520 on a scientific calculator, enter 1.015, then press the key, then enter 20, then press the key.

A typical calculator displays a maximum of ten digits. Therefore, we will initially show ten digits in our calculations.

Because the number displayed is not exact, we use the symbol instead of =. The symbol means “approximately equal to.”

All Right Reserved. Copyright 2005-2023