SIMPLE INTEREST & COMPOUND INTEREST & SURDS & INDICES
The formula for calculating simple interest is:
Simple Interest = (Principal x Interest Rate x Time)/100
= (P x R X T)/100
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.
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!
We recall that a power is the product of a certain number of factors, all of which are the same. For example, 37 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.
- To divide powers with the same base, subtract the indices.
= am − n, (provided m > n.)
- To raise a power to a power, multiply the indices.
- A power of a product is the product of the powers.
- A power of a quotient is the quotient of the powers.
(provided b≠ 0.)