Armando put $78 into a CD that pays 4.9% interest. According to the rule of
2 answers:
It will take 14.7 years for Armando's money to double.
Option C
<u>Explanation:</u>
The rule of 72 is generally used to estimate the number of years required to double the invested money at a given annual rate of return. And alternatively to find the number of years required to double the money at a given interest rate, we have to just divide the interest rate into 72.
Here, the interest rate is 4.9%. Therefore, it would be as follows
Rule 72 can be used to identify the following:
- Number of years it takes an investment to double,
- Number of years it takes debt to double,
- The interest rate must earn to double in a time frame,
- Number of times debt or money will double in a period of time.
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Answer:
Step-by-step explanation:
Consider the revenue function given by . We want to find the values of each of the variables such that the gradient( i.e the first partial derivatives of the function) is 0. Then, we have the following (the explicit calculations of both derivatives are omitted).
From the first equation, we get, .If we replace that in the second equation, we get
From where we get that . If we replace that in the first equation, we get
So, the critical point is . We must check that it is a maximum. To do so, we will use the Hessian criteria. To do so, we must calculate the second derivatives and the crossed derivatives and check if the criteria is fulfilled in order for it to be a maximum. We get that
We have the following matrix,
.
Recall that the Hessian criteria says that, for the point to be a maximum, the determinant of the whole matrix should be positive and the element of the matrix that is in the upper left corner should be negative. Note that the determinant of the matrix is and that -10<0. Hence, the criteria is fulfilled and the critical point is a maximum