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Mariulka [41]
3 years ago
11

the discriminant in an equation derived directly from the quadratic formula is positive the variable value represented by the qu

adratic formula has what possible real value
Mathematics
1 answer:
nordsb [41]3 years ago
3 0
Let d=discriminant.  The the rule is:

d>0, there are two real solutions

d=0, there is one real solution

d<0, there is no real solutions (but there are two imaginary solutions)

So if it is positive, there are two real solutions.
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Find the future value and interest earned if $8704.56 is invested for 8 years at 4% compounded (a) semiannually and (b) continuo
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a) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded 2 times per year over 8 years is <u>$11,949.50</u>.

b) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is <u>$11,987.29</u>.

<h3>How is the future value determined?</h3>

The future value can be determined using an online finance calculator.

Data and Calculations:

<h3>a) Compounded Semiannually:</h3>

Principal (P): $8,704.56

Annual Rate (R): 4%

Compound (n): Compounding Semi-Annually

Time (t in years): 8 years

<u>Result</u>:

A = $11,949.50

A = P + I where

P (principal) = $8,704.56

I (interest) = $3,244.94

<h3>Calculation Steps:</h3>

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 8,704.56(1 + 0.04/2)(2)(8)

A = 8,704.56(1 + 0.02)(16)

A = $11,949.50

<h3>b) Compounded Continuously:</h3>

Using the formula A = Pert

Principal (P):  $8,704.56

Annual Rate (R): 4%

Compound (n): Compounding Continuously

Time (t in years):   8 years

<u>Result</u>:

A = $11,987.29

A = P + I where

P (principal) = $8,704.56

I (interest) = $3,282.73

<h3>Calculation Steps:</h3>

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A, using the mathematical constant, e = 2.71828

A = Pert

A = 8,704.56(2.71828)(0.04)(8)

A = $11,987.29

Thus, while the future value of $8,704.56 at a rate of 4% per year compounded semiannually over 8 years is <u>$11,949.50</u>,  the future value of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is <u>$11,987.29</u>.

Learn more about compounding interest at brainly.com/question/24274034

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