John invested $3,000 for 5 years at nominal rate 8%, compounded quarterly. What is the accumulated value at the end of 5 years? What is the annual effective rate of interest?
A=P(1 + R/N) NT
=3000(1+ 0.08/4) 4*5
4457.84
4457.84/5
1[ 4457.84/3000] 1/5
= 0.0824
Answer is 8.24%
Mike and Kathy purchased their home at the price of $250,000. They paid $20,000 as down payment and took a mortgage for the balance. The mortgage is for thirty years and has an annual interest rate of 9%, compounded monthly. What are the monthly payments on the mortgage?
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A=p(1 + R/N) NT
=250000-20000=230000
=230000(1+0.09/12) 360
=$3388032.51
3388032.51/(360)
Answer = $9411
3) Write the augmented matrix corresponding to the system of equations and then using Gauss-Jordan elimination method to solve the system
2x +3y =-1
x - y = 2.
[2 3] [-1]
[1 -1] [2]
=[1][0]x
[0][1]y
R1 = 1/2r1
R1 = -r1+r2
½ +2 – 5/2
R2= -2/5r2
R1 = -3/2(r2)+r1
=-3/2(-1)+=1/2
= 3/2-1/3
= 1
Therefore, [1 , 0]
[0 . 1]=[1, -1]
Answer:
X=1
Y=-1
4) Let
A = [ 3, -1] B= [2, 1]
[ 5, ,-2], [-1, 3]
Find 3A - B.
3(3 , -1: 3 , -2) – (2 , -1: 2, -1,3)
Answer = (7 , -4 )
(14, -9)
Find the inverse of A.
3(-2) – 5(-1)
=-1
=-1/1(-2,-5:1,3)
The inverse is (2 , -1)
(5 , 3)
c. Find A∙B.
= 6+1 , 3-3: 10+2, 5-6
Answer
= (7 , 0)
(12 , -1)
5) A random sample of 200 adults are classified below by sex and their level of education attained.
Education Male Female
Elementary 38 45
Secondary 28 50
College 22 17
If a person is picked at random from this group, find the probability that
(a). the person has a secondary education
(28+50)/200
Answer:
= 78/200
(b) the person has a college degree, given that the person is a female.
=17/200
6) A class of 20 students took a 5-point math quiz. The following frequency distribution describes the scores received on the quiz.
|
Score x |
0 |
1 |
2 |
3 |
4 |
5 |
|
Probability |
0.05 |
0.05 |
0.15 |
0.4 |
0.25 |
0.1 |
Find the probability that a randomly selected student got a score more than 3.
Find the Expected value of this distribution.
=0*0.05 + 1*0.05 + 2*0.15 + 3*0.4 +4*0,25 + 5*0.1
= 61/20
Find the variance and standard deviation
0 2 *0.05 + 1 2 *0.05 + 2 2 *0.15 + 3 2 *0.4 +4 2 *0,25 + 5 2 *0.1
=43/4
43/4 – (61/20) 2
= Variance is 579/400
= Standard deviation is the square root of variance which gives 1.2031
7) According to the Cellular Telecommunications Industry Association, the average local monthly cell phone bill is $42. Suppose local monthly cell phone bills are normally distributed with a standard deviation $12. What is the probability that a randomly selected cell phone bill is between $30 and $55?
Probability of 30 0r less 0.15866
Probanility of 50 or more 0.25249
Probability (between 30 and 50)= 0.58885
