If i have $500 and I get 5% interest compounded annually how much would i have after 10 years

$814.45

Step-by-step explanation:

This is the formular: A=P(1+rn)n⋅t

A = total amount

P = principal or amount of money deposited,

r = annual interest rate

n = number of times compounded per year

t = time in years

A= $500 (1+5%/1)1.10

$500 (1+0.05) 10

$500 × 1.629

=$814.45

step   1   :

            2

simplify   ——

            v2

equation at the end of step   1   :

                  2            

  • (v2)) -   -   5v) +   4

                  v2            

step   2   :

equation at the end of step   2   :

            2            

  ((2v2 -   -   5v) +   4

          v2            

step   3   :

rewriting the whole as an equivalent fraction :

3.1   subtracting a fraction from a whole

rewrite the whole as a fraction using   v2   as the denominator :

            2v2     2v2 • v2

    2v2 =     =  

            1         v2  

equivalent fraction : the fraction thus generated looks different but has the same value as the whole

common denominator : the equivalent fraction and the other fraction involved in the calculation share the same denominator

adding fractions that have a common denominator :

3.2       adding up the two equivalent fractions

add the two equivalent fractions which now have a common denominator

combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2v2 • v2 - (2)     2v4 - 2

  =  

      v2             v2  

equation at the end of step   3   :

  (2v4 - 2)          

  -   5v) +   4

      v2              

step   4   :

rewriting the whole as an equivalent fraction :

4.1   subtracting a whole from a fraction

rewrite the whole as a fraction using   v2   as the denominator :

          5v     5v • v2

    5v =   ——   =  

          1         v2  

step   5   :

pulling out like terms :

5.1     pull out like factors :

  2v4 - 2   =   2 • (v4 - 1)

trying to factor as a difference of squares :

5.2       factoring:   v4 - 1

theory : a difference of two perfect squares,   a2 - b2   can be factored into   (a+b) • (a-b)

proof :   (a+b) • (a-b) =

        a2 - ab + ba - b2 =

        a2 - ab + ab - b2 =

        a2 - b2

note :   ab = ba is the commutative property of multiplication.

note :   - ab + ab equals zero and is therefore eliminated from the expression.

check : 1 is the square of 1

check :   v4   is the square of   v2

factorization is :       (v2 + 1)   •   (v2 - 1)

polynomial roots calculator :

5.3     find roots (zeroes) of :       f(v) = v2 + 1

polynomial roots calculator is a set of methods aimed at finding values of   v   for which   f(v)=0  

rational roots test is one of the above mentioned tools. it would only find rational roots that is numbers   v   which can be expressed as the quotient of two integers

the rational root theorem states that if a polynomial zeroes for a rational number   p/q   then   p   is a factor of the trailing constant and   q   is a factor of the leading coefficient

in this case, the leading coefficient is   1   and the trailing constant is   1.

the factor(s) are:

of the leading coefficient :   1

of the trailing constant :   1

let us test

  p     q     p/q     f(p/q)     divisor

      -1       1         -1.00         2.00    

      1       1         1.00         2.00    

polynomial roots calculator found no rational roots

trying to factor as a difference of squares :

5.4       factoring:   v2 - 1

check : 1 is the square of 1

check :   v2   is the square of   v1

factorization is :       (v + 1)   •   (v - 1)

adding fractions that have a common denominator :

5.5       adding up the two equivalent fractions

2 • (v2+1) • (v+1) • (v-1) - (5v • v2)     2v4 - 5v3 - 2

  =  

                  v2                             v2      

equation at the end of step   5   :

  (2v4 - 5v3 - 2)    

  +   4

        v2          

step   6   :

rewriting the whole as an equivalent fraction :

6.1   adding a whole to a fraction

rewrite the whole as a fraction using   v2   as the denominator :

        4     4 • v2

    4 =   —   =  

        1       v2  

polynomial roots calculator :

6.2     find roots (zeroes) of :       f(v) = 2v4 - 5v3 - 2

    see theory in step 5.3

in this case, the leading coefficient is   2   and the trailing constant is   -2.

the factor(s) are:

of the leading coefficient :   1,2

of the trailing constant :   1 ,2

let us test

  p     q     p/q     f(p/q)     divisor

      -1       1         -1.00         5.00    

      -1       2         -0.50         -1.25    

      -2       1         -2.00         70.00    

      1       1         1.00         -5.00    

      1       2         0.50         -2.50    

      2       1         2.00         -10.00    

polynomial roots calculator found no rational roots

adding fractions that have a common denominator :

6.3       adding up the two equivalent fractions

(2v4-5v3-2) + 4 • v2     2v4 - 5v3 + 4v2 - 2

  =  

          v2                       v2        

checking for a perfect cube :

6.4     2v4 - 5v3 + 4v2 - 2   is not a perfect cube

trying to factor by pulling out :

6.5       factoring:   2v4 - 5v3 + 4v2 - 2

thoughtfully split the expression at hand into groups, each group having two terms :

group 1:   4v2 - 2

group 2:   2v4 - 5v3

pull out from each group separately :

group 1:   (2v2 - 1) • (2)

group 2:   (2v - 5) • (v3)

bad news factoring by pulling out fails :

the groups have no common factor and can not be added up to form a multiplication.

polynomial roots calculator :

6.6     find roots (zeroes) of :       f(v) = 2v4 - 5v3 + 4v2 - 2

    see theory in step 5.3

in this case, the leading coefficient is   2   and the trailing constant is   -2.

the factor(s) are:

of the leading coefficient :   1,2

of the trailing constant :   1 ,2

let us test

  p     q     p/q     f(p/q)     divisor

      -1       1         -1.00         9.00    

      -1       2         -0.50         -0.25    

      -2       1         -2.00         86.00    

      1       1         1.00         -1.00    

      1       2         0.50         -1.50    

      2       1         2.00         6.00    

polynomial roots calculator found no rational roots

final result :

  2v4 - 5v3 + 4v2 - 2

          v2        

hope this

give me brainliest