Please help!!!
1 answer:
Answer:
Step-by-step explanation:
<u>Compound Interest</u>
It's the type of financial calculations that includes the interest of previous periods into the new interests earned by some initial investment or principal P.
If we want to compute the final value FV of a series of n payments R at a fixed compound interest rate i, then
Where
The question provides us the following data
i=10% compounded twice a year
n=3 1/2 years
FV=15,000
We need to convert the number of periods and the interest rate to a semester base:
Let's calculate Fm
Knowing that
Solving for R
Sara should deposit $1,842.30 twice a year to have the down payment for her own restaurant
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Answer with explanation:
Let us assume that the 2 functions are:
1) f(x)
2) g(x)
Now by definition of concave function we have the first derivative of the function should be strictly decreasing thus for the above 2 function we conclude that
Now the sum of the 2 functions is shown below
Diffrentiating both sides with respect to 'x' we get
Since each term in the right of the above equation is negative thus we conclude that their sum is also negative thus
Thus the sum of the 2 functions is also a concave function.
Part 2)
The product of the 2 functions is shown below
Diffrentiating both sides with respect to 'x' we get
Now we can see the sign of the terms on the right hand side depend on the signs of the function's themselves hence we remain inconclusive about the sign of the product as a whole. Thus the product can be concave or convex.