compound interest

(noun)

Interest, as on a loan or a bank account, that is calculated on the total on the principal plus accumulated unpaid interest.

Related Terms

Examples of compound interest in the following topics:

  • Interest Compounded Continuously

    • Compound interest is accrued when interest is earned not only on principal, but on previously accrued interest: it is interest on interest.
    • In compound interest, interest is accrued on both the principal and on prior interest earned.
    • Compound interest is not linear, but exponential in form.
    • This time we use compound interest instead.
    • You earn the most interest when interest is compounded continuously.

  • The Number e

    • One of the many places the number $e$ plays a role in mathematics is in the formula for compound interest.
    • Jacob Bernoulli discovered this constant by asking questions related to the amount of money in an account after a certain number of years, if the interest is compounded $n$ times per year.
    • He was able to come up with the formula that if the interest rate is $r$ percent and is calculated $n$ times per year, and the account originally contained $P$ dollars, then the amount in the account after $t$ years is given by $A=P(1+{r \over n})^{nt}.$ By then asking about what happens as $n$ gets arbitrarily large, he was able to come up with the formula for continuously compounded interest, which is $A=Pe^{rt}

  • Introduction to Exponents

    • Exponentiation is used frequently in many fields, including economics, biology, chemistry, physics, and computer science, with applications such as compound interest, population growth, chemical reaction kinetics, wave behavior, and public key cryptography.

  • Logarithmic Functions

    • The irrational number  $e\approx 2.718 $ arises naturally in financial mathematics, in computations having to do with compound interest and annuities.

  • Problem-Solving

    • Compound interest at a constant interest rate provides exponential growth of the capital.

  • Common Bases of Logarithms

    • The irrational number  $e\approx 2.718 $ and arises naturally in financial mathematics in computations having to do with compound interest.

  • Compound Inequalities

    • A compound inequality involves three expressions, not two, but can also be solved to find the possible values for a variable.
    • The compound inequality $a < x < b$ indicates "betweenness"—the number $x$ is between the numbers $a$ and $b$.
    • Solve a compound inequality by balancing all three components of the inequality

  • Formulas and Problem-Solving

    • For example, one can use a linear equation to determine the amount of interest accrued on a home equity line of credit after a given amount of time.
    • Consider the hypothetical situation in which you need money to make home improvements and can open a $20,000 credit line at an interest rate of 2.5% per year.
    • Where I is interest, p is the principal amount loaned ($20,000), r is the interest rate (2%, or 0.02) per year, and T is the number of years elapsed (15 months will be 1.25 years).
    • Plugging the known values into the above formula, we can determine that you will pay $500 in interest.

  • Population Growth

    • The ratio of t to f is often simplified into one value representing the number of compounding cycles.

  • Graphs of Exponential Functions, Base e

    • The function $f(x) = e^x$ is a basic exponential function with some very interesting properties.