Equations – Inequalities - Compound Interest Formulas

Minggu, 29 Maret 2020

Equations

Real numbers: a, b, c, p, q, u, v

Solution: x₁, x₂, y₁, y₂, y₃




1.  Linear Equation in One Variable

   

2.   Quadratic Equation

   

3.   Discriminant
      D = b² – 4ac

4.   Viete’s Formulas

 If x² + px + q = 0, then

    

5.   ax² + bx = 0,.

6.   ax² + bx = 0,.

7.   Cubic Equation, Cardano’s Formula.

        y³ + py + q = 0,

       

Inequalities

Variables: x, y, z

Real numbers:, m, n

Determinants: D, D_x, D_y, D_z

1.   Inequaities,Interval Notations and Graphs

2.   If a > b, then b < a.

3.   If a > b, then a – b > 0 or b – a  < 0.

4.   If a > b, then a + c > b – c.  

5.   If a > b, then a – c > b + c. 

6.   If a > b and c > d , then a + c > b + d.

7.   If a > b and c > d , then a – d > b – c.

8.   If a > b and m > 0, then ma > mb. 

9.  

10.  If a > b and m < 0, then ma < mb. 
11.

12.  If 0 < a < b and n > 0, then aⁿ < bⁿ.

13.  If 0 < a < b and n < 0, then aⁿ > bⁿ.

19.  ax² + bx + c < 0

20.  │a + b│≤ │a│+ │b│

21.  If │x│< 0,  then 1 – a < x < a, where a > 0.

22.  If │x│> 0,  then x < – a and x > a, where a > 0.

Compound Interest Formulas

Future value: A

Initial deposit: C

Annual rate of interest: r

Number of year invested: t

Number of times compounded per year: n

1.   General Compound Interest Formula

    

2.   Simplified Compound Interest Formula

If interest is compounded once per year, then the previous formula simplifies to:

A = C(1 + r)^t.

3.   Continuous Compound Interest

      If interest is compounded continually (n → ∞), then A = Ce^rt.

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Labels: Mathematician

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