Annual interest

Definition

Annual interest is the percentage of an investment or loan amount that is paid as interest over one year. It can be calculated using simple or compound interest formulas.

5 Must Know Facts For Your Next Test

1. Simple annual interest is calculated using the formula $I = P \cdot r \cdot t$, where $I$ is the interest, $P$ is the principal amount, $r$ is the annual interest rate, and $t$ is the time in years.
2. Compound annual interest considers interest on both the initial principal and the accumulated interest from previous periods: $A = P (1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest.
3. In a geometric series context, compound interest can be modeled by a series where each term represents the balance at a given compounding period.
4. The concept of annual percentage yield (APY) accounts for compounding within a year to give an effective yearly rate.
5. When working with sequences and series, understanding how to sum geometric sequences helps in calculating total amounts for investments with regular contributions.

Review Questions

• What formula would you use to calculate simple annual interest?
• How does compound annual interest differ from simple annual interest?
• How can geometric sequences help model compound interests?

Related terms

Principal: The initial sum of money invested or loaned before any interest.

Compound Interest: Interest calculated on both the initial principal and also on the accumulated interest from previous periods.

Geometric Series: A sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.