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The polynomial that gives the interest earned after a year will have variables, exponents and constants that are joined by operators.
- The interest earned after one year is <u>0.018·x</u>
Reasons:
The amount Paul has to invest = $900
The annual interest rate from the savings account = 1.8%
The amount the money market account pays per year = 4.2 %
Required: The polynomial for the interest Paul earned by investing <em>x</em> dollars in the savings account.
Solution:
The interest earned is found using the compound interest formula as follows;
Where;
A = The amount in the account after one year
P = The original amount invested = x
r = The interest rate offered on the investment = 1.8% = 0.018
t = The time of the investment = 1 year
n = The number of times of application of the interest per period = Once per year
Which gives;
Interest = Amount earned = A - P
Therefore;
Plugging in the values gives;
The polynomial equation is therefore;
Interest, I = 0.018·x
Using the simple interest formula, we have;
Which gives;
Interest earned by investing in the savings account for one year, I = 0.018·x
- The polynomial representing the interest earned is <u><em>I</em></u><u> = 0.018·x</u>
Learn more here:
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Explanation:
When something is subtracted from both sides of the equation, the justification is the <em>subtraction property of equality</em>. When something multiplies both sides of the equation, the justification is the <em>multiplication property of equality</em>. (This should not be a mystery.)
Here, the equation is solved by subtracting 17/3, then subtracting 1/2x, then multiplying by the inverse of the coefficient of x. After each of these steps is a simplification.