Compound Interest

Important Words

Principal

The amount of money being loaned or borrowed.

Interest

The "price" for loaning or borrowing.

Rate

The percentage of the principal that will be used to calculate interest.

Term

How long the loan goes for.

per annum

"each year" (Latin).

Compound Interest

A specific way to calculate interest, based on the value of the investment/loan as it changes.

Important Formulas

The following formulas use these variables:

• I is the interest;
• P is the principal (the original amount);
• F is the final amount;
• r is the interest rate per annum (as a percent);
• t is the term (the number of years of the investment/loan);
• n is the number of interest periods per year.

To find the final amount of an investment or loan:

(1)

\begin{align} F = P \times \left( 1 + \frac{r}{100} \right) ^{t} \end{align}

To find the interest of an investment or loan:

(2)

\begin{align} I = F - P = P \times \left( 1 + \frac{r}{100} \right) ^{t} - P \end{align}

To find the final amount of an investment or loan for which interest is calculated other than annually:

(3)

\begin{align} F = P \times \left( 1 + \frac{r/n}{100} \right) ^{(n \times t)} \end{align}

where n is given in the following table:

Interest is calculated…	n
annually	1
quarterly	4
monthly	12
fortnightly	26
weekly	52
daily	365

To find the principal of an investment or loan:

(4)

\begin{align} P = \frac{F}{\left( 1 + \frac{r/n}{100} \right) ^{(n \times t)}} \end{align}

References

Jones, et al. Essential Standard General Mathematics, Cambridge University Press, First Edition (2005), pp222-228.