By applying the formulas of present and future values of annuity we can solve this problem. In this mortgage problem, first we have to find loan amount after the down payment. It is 699,000 - 699,000 * 0.2 = 559,200$. We have to set it as PV (Present Value) of annuity. Using the PV formula ![PV = A \frac{[1- \frac{1}{(1+r)^{N}}]}{r}](https://tex.z-dn.net/?f=%20PV%20%3D%20A%20%5Cfrac%7B%5B1-%20%5Cfrac%7B1%7D%7B%281%2Br%29%5E%7BN%7D%7D%5D%7D%7Br%7D%20)
, we first find A, which is an annual payment. Exact calculation with mortgage calculator gives us A = 33,866.56$. After finding it, plugging this number into FV (Future Value) formula ![FV = A\frac{[(1+r)^{N}-1]}{r}](https://tex.z-dn.net/?f=%20FV%20%3D%20A%5Cfrac%7B%5B%281%2Br%29%5E%7BN%7D-1%5D%7D%7Br%7D%20%20%20)
, we find the value of the future value and it is 1,185,329.66$. And the total financial charge is 1,185,329.66 - 559,200 = 626,129.66$
Answer:
a) P ( 3 ≤X≤ 5 ) = 0.02619
b) E(X) = 1
Step-by-step explanation:
Given:
- The CDF of a random variable X = { 0 , 1 , 2 , 3 , .... } is given as:
Find:
a.Calculate the probability that 3 ≤X≤ 5
b) Find the expected value of X, E(X), using the fact that. (Hint: You will have to evaluate an infinite sum, but that will be easy to do if you notice that
Solution:
- The CDF gives the probability of (X < x) for any value of x. So to compute the P ( 3 ≤X≤ 5 ) we will set the limits.
- The Expected Value can be determined by sum to infinity of CDF:
E(X) = Σ ( 1 - F(X) )
E(X) = Limit n->∞ [1 - 1 / ( n + 2 ) ]
E(X) = 1
Answer:
Life Path
Step-by-step explanation:
It's two words, and they are both of equal length. I hope that helps.
