**SIMPLE INTEREST & COMPOUND INTEREST & SURDS & INDICES**

**Simple Interest**

The formula for calculating simple interest is:

Simple Interest = (Principal x Interest Rate x Time)/100

= (P x R X T)/100

**Compound Interest**

The formula for calculating compound interest is:

Compound Interest = Total amount of Principal (P) and Interest in future (or Future Value,”I”) less Principal amount at present (or Present Value)

= [P (1 + I)^{ T}] – P

= P [(1 + I)^{ T} – 1]

Where P = Principal, I = annual interest rate in percentage terms, and

T = number of compounding periods.

**Surds**

When we can’t simplify a number to remove a square root (or cube root etc) then it is a surd.

Example: √2 (square root of 2) can’t be simplified further so it is a surd

Example: √4 (square root of 4) can be simplified (to 2), so it is not a surd!

**INDICES**

We recall that a **power **is the product of a certain number of factors, all of which are the same. For example, 3^{7} is a power, in which the number 3 is called the **base **and the number 7 is called the **index** or **exponent**.

In the module, **Multiples, Factors and Powers**, the following index laws were established for **positive **integer** **exponents. So positive integers and , and rational numbers and , we have:

- To multiply powers with the same base, add the indices.

*a*=^{m}a^{n}*a*^{m}^{+n} - To divide powers with the same base, subtract the indices.

=*a*^{m }^{− n}, (provided*m*>*n*.) - To raise a power to a power, multiply the indices.

(*a*)^{m}=^{n}*a*^{mn} - A power of a product is the product of the powers.

(*ab*)=^{m}*a*^{m}b^{m} - A power of a quotient is the quotient of the powers.

(provided*b*≠ 0.)