The table below shows the future value of a certificate of deposit (CD) after x years Eric states the applied interest is simple
interest true or false?
2 answers:
Answer:
Option B.
Step-by-step explanation:
Eric states the applied interest is simple interest. We need to check whether the this statement is true or false.
In simple interest, the amount of deposit increased at a constant rate. It means the difference between future values of any two consecutive years will same.
Difference between future values of first two years.
Difference between future values of 2nd and 3rd year is
Since d₁≠d₂, therefore, the given statement is false.
Thus, the correct option is B.
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Explanation:
In order to prove that affirmation, we define the function g over the interval [0, 1/2] with the formula
If we evaluate g at the endpoints we have
g(0) = f(1/2)-f(0) = f(1/2) - f(1) (because f(0) = f(1))
g(1/2) = f(1) - f(1/2) = -g(0)
Since g(1/2) = -g(0), we have one chance out of three
- g(0) > 0 and g(1/2) < 0
- g(0) < 0 and g(1/2) > 0
- g(0) = g(1/2) = 0
We will prove that g has a zero on [0,1/2]. If g(0) = 0, then it is trivial. If g(0) ≠ 0, then we are in one of the first two cases, and therefore g(0) * g(1/2) < 0. Since f is continuous, so is g. Bolzano's Theorem assures that there exists c in (0,1/2) such that g(c) = 0. This proves that g has at least one zero on [0,1/2].
Let c be a 0 of g, then we have
Hence, f(c+1/2) = f(c) as we wanted.