Interest is the cost of borrowing money or the reward for saving it. It's typically expressed as a percentage of the principal amount (the original sum of money) over a specific period, usually a year.
Simple Interest vs. Compound Interest
There are two main types of interest: simple and compound.
Simple Interest
Simple interest is calculated only on the principal amount. The formula for simple interest is:
\[A = P(1 + rt)\]
Where:
\(A\) = Final amount
\(P\) = Principal amount
\(r\) = Annual interest rate (in decimal form)
\(t\) = Time in years
Compound Interest
Compound interest is calculated on the principal and also on the accumulated interest of previous periods. The formula for compound interest is:
\[A = P(1 + \frac{r}{n})^{nt}\]
Where:
\(A\) = Final amount
\(P\) = Principal amount
\(r\) = Annual interest rate (in decimal form)
\(n\) = Number of times interest is compounded per year
\(t\) = Time in years
Step-by-Step Interest Calculation
Identify the principal amount (P), annual interest rate (r), and time period (t).
Convert the annual interest rate to decimal form (divide by 100).
For compound interest, determine the compounding frequency (n).
Apply the appropriate formula (simple or compound).
Calculate the final amount (A).
Subtract the principal from the final amount to get the interest earned.
Example Calculation
Let's calculate the interest for a principal of $1,000, an annual interest rate of 5%, over 2 years, compounded annually: