A couple purchased a home and signed a mortgage contract for $900,000 to
be paid with half-yearly payments over a 25-year period. The interest rate
applicable is j2 = 5.5% p.a. applicable for the first five years, with the condition
that the interest rate will be increased by 12% every 5 years for the remaining
term of the loan.
(a) Calculate the half-yearly payment required for each five-year interval
Answers
9514 1404 393
Answer:
$33,336.83$35,176.68$36,869.23$38,266.75$39,158.08Step-by-step explanation:
The amortization formula can be used to find the payment value.
A = P(r/2)/(1 -(1 +r/2)^(2n))
where P is the principal amount at the beginning of the loan period, r is the annual interest rate, n is the number of years remaining on the loan
The value of A in this scenario is the semi-annual payment.
Initially, the interest rate is 0.055 and the number of years remaining is 25.
After the first 5-year period, the interest rate goes up by 12%, so is multiplied by a factor of 1.12 to become 6.16% per year. The same growth factor is applied to the interest rate at the beginning of each 5-year period.
Of course, the number of years remaining is decreased by 5 years at the beginning of the next 5-year period.
__
The Principal remaining at the end of each 5-year period is the starting principal for the next period. It is calculated from ...
FV = P(1 +r/2)^10 -A((1 +r/2)^10 -1)/(r/2)
Where P is the starting principal, A is the loan payment as calculated above, and r is the annual interest rate.
__
These formulas are built into spreadsheet functions, so the desired set of loan payments can be calculated easily by that technology. The result is attached. In the "# pmts" column is the value used to amortize the loan for the 5-year period. The semiannual payment is calculated as though the loan would be completely paid off in that number of payments, keeping the same interest rate for the duration. Of course, that payment series is interrupted and the loan recalculated at the beginning of the next 5 years.
The half-yearly payments for each 5-year interval are ...
$33,336.83
$35,176.68
$36,869.23
$38,266.75
$39,158.08
_____
Additional comment
The values displayed in the spreadsheet are rounded to the values shown. The values used in calculation have 14 or more significant digits. This means the numbers here may vary from those provided by a lending institution. In the real world, the principal and interest values are rounded to cents with each payment, so actual results may vary by a few cents either way.
Related Questions
Will choose brainliest! Please help! (This is Khan Academy)
Answers
Answer:
Option B. A = (5/6)^-⅛
Step-by-step explanation:
From the question given above, we obtained:
(5/6)ˣ = A¯⁸ˣ
We can obtain the value of A as follow:
(5/6)ˣ = A¯⁸ˣ
Cancel x from both side
5/6 = A¯⁸
Recall:
M¯ⁿ = 1/Mⁿ
A¯⁸ = 1/A⁸
Thus,
5/6 = 1/A⁸
Cross multiply
5 × A⁸ = 6
Divide both side by 5
A⁸ = 6/5
Take the 8th root of both sides
A = ⁸√(6/5)
Recall
ⁿ√M = M^1/n
Thus,
⁸√(6/5) = (6/5)^⅛
Therefore,
A = (6/5)^⅛
Recall:
(A/B)ⁿ = (B/A)¯ⁿ
(6/5)^⅛ = (5/6)^-⅛
Therefore,
A = (5/6)^-⅛
The ratio of boys to girls in Mr. Johnsons after school club is the same as the ratio is the same to the ratio of boys to girls in Mr. Greene's after school club. There are 4 boys and 12 girls in Mr. Johnsons club. There are 6 boys in Mr. Greene's club. How many girls are in Ms. Greene's club?
Answers
Answer:
18 GIRLS
Step-by-step explanation:
1. Lets write a fraction (4 boys/12 girls)
[tex]\frac{4 \\boys}{12 \\ \\girls}[/tex]
2. Now lets plug the value in
[tex]\frac{6 \\boys}{x girls}[/tex]
3. In the original equation, the amount of girls is 3 times the amount of boys
4. multiply 6 and 3 = 18
5. 18 girls
Answer:
18 <3
Step-by-step explanation:
find the missing angle measure in each triangle. Then classify the triangle as acute, right, or obtuse. PLEASE ANSWER QUICK ILL MARK BRAINLIEST
Answers
Answer:
Step-by-step explanation:
17
Answer: The missing angle is 32 degrees.
Step-by-step explanation: All the degrees in a triangle sum up to 180 degrees. Add the two known angles and subtract the sum from 180
Hope this helps! :)
Round the decimal to the nearest hundreth. If decimal cannot be rounded, state this.
194.59
Answers
The decimal cannot be rounded. It is already rounded to the nearest hundredth.
explain whether 8t - 3y - 4t is equivalent to 7t +(-3t) - 3y.
Answers
Answer:
4t - 3y
Step-by-step explanation:
8t - 3y - 4t
8t - 4t - 3y
4t - 3y
7t +(-3t) - 3y
7t - 3t - 3y
4t - 3y
Answer:
These expressions are equivalent, as both of them simplify down to (4t - 3y).
Step-by-step explanation:
In order to determine if (8t - 3y - 4t) is equivalent to (7t + (-3t) - 3y) one must simplify each equation. Combine like terms by performing the operations between the coefficients of the variables.
8t - 3y - 4t
= 4t - 3y
7t + (-3t) - 3y
= 7t - 3t - 3y
= 4t - 3y
please help i’ll give brainliest
7.)What is the maximum number of texts received?
8.)All of the following are true except -
A.The range of the data is 190.
B.At least one student received no texts at all.
C.Most of the students received 65 or fewer texts.
D.50% of students received between 65 and 160 text messages.
9.)Which of the following cannot be determined from analyzing the boxplot?
A.
Mean
B.
Median
O.
Minimum D.
Range
10.) What percent of students receive more than 65 texts in a single day?
Answers
Answer:
7. 190
8. C
9. A
10. ~66% (not sure about this one though)
Step-by-step explanation:
How stopwatch can measure accurate reading?
Answers
answer in picture
stay safe (..
Answer:
Hello There!!
Step-by-step explanation:
Reading gives the required time interval.Some precise stopwatches are electronically connected to the time event.Therefore, making it more accurate.
hope this helps,have a great day!!
~Pinky~
Find the ratio of A to B if A= 51,786 and B= 17,475
Answers
Answer:
[tex]\frac{17262}{5825}[/tex]
Step-by-step explanation:
A ratio is another way of expressing a fractional value. One can express a ratio as a fraction. This problem asks one to find the ratio of (A) to (B). Set this up as a fraction, then substitute the given values in and simplify,
[tex]\frac{A}{B}[/tex]
The following information is given.
[tex]A=51786\\B=17475[/tex]
Substitute these values into the problem,
[tex]=\frac{51786}{17475}[/tex]
Both numbers are divisible by (3), thus reduce the ratio,
[tex]=\frac{17262}{5825}[/tex]
Since they have no other factors in common, the final answer is the following,
[tex]=\frac{17262}{5825}[/tex]
The domain of a function is what?
Answers
The domain is all possible x values, specified for that function.
convert 0.13 into a fraction
Answers
Find the value of x in the figure
Answers
Answer:
x = 100
Step-by-step explanation:
180-57 would equal 123 which means 123 = x +23 and you can simplify this equation by moving 23 over to 123 and subtracting them leaving x = 100
123 = x+ 23
-23 + 123 = x
100 = x
x = 100
sorry, i'm really bad at explaining
180 degree angles when added
180-57 (for known angle)= 123
x+23=123<- we need to take off the all known angles to get x
123-123=100
x=100 is the answer
Innocent until proven guilty? In Japanese criminal trials, about 95% of the defendants are found guilty. In the United States, about 60% of the defendants are found guilty in criminal trials. Suppose you are a news reporter following four criminal trials.
a) If the trials were in Japan, what is the probability that all the defendants would be found guilty? What is the probability if the trials were in the United States?
b) Of the four trials, what is the expected number of guilty verdicts in Japan? What is the expected number in the United States? What is the standard deviation in Japan? What is the standard deviation in the United States?
c) As a U.S. news reporter, what is the smallest number of trials n you would need to cover to be at least 99% sure of two or more convictions? What is the smallest number of trials n you would need if you covered trials in Japan?
Answers
Step-by-step explanation:
Let X be the number of guilty defendants in Japan
Let y be the number in the US
we have n = 4
p = 0.95
a.) prob of trials in Japan
p(x=4)
= 0.95⁴
= 0.8145
prob of trials in US
p(X=4)
= 0.60⁴
= 0.1296
B. expected number in Japan
E(X) = n*p
= 4*0.95
= 3.8
we find the variance
= n*p(1-p)
= 4*0.95(1-0.95)
= 0.19
standard deviation for japan
= √0.19
= 0.4359
expected number for US
E(X) = n*p
= 4*0.60
= 2.4
we find the variance
= n*p(1-p)
= 4*0.60(1-0.6)
= 0.96
standard deviation for US
= √0.96
= 0.979
c. 2*4 = 8
What is the coordinate point of letter F
Answers
Explanation: When finding the coordinates of a point, first look at its position on the X axis (horizontal axis). The point F lies on the “-6” marking on this axis. Now, look at the point’s position on the Y axis (vertical axis). Point F lies on the “-1” marking on the Y axis. Now that you have both X and Y values of the point, you can write it in the final format: (X, Y) ——> (-6, -1)
Hope that helps シ
Complete the remainder of the
table for the given function rule
Answers
Answer:
y = 3
y = 2
y = 1
y = 0
Step-by-step explanation:
Given expression;
y = (-x/3) + 2
Find:
Value of y, if x = -3Value of y, if x = 0Value of y, if x = 3Value of y, if x = 6Computation:
Value of y, if x = -3
y = (-x/3) + 2
y = (3/3) + 2
y = 3
Value of y, if x = 0
y = (-x/3) + 2
y = (-0/3) + 2
y = 2
Value of y, if x = 3
y = (-x/3) + 2
y = (-3/3) + 2
y = 1
Value of y, if x = 6
y = (-x/3) + 2
y = (-6/3) + 2
y = 0
When the mean value of the dependent variable is independent of variation in the independent variable, the slope of the regression line is:________
Answers
Answer:
zero
Step-by-step explanation:
The optimally fitted straight line via the locations and points on a graph is determined via linear regression. You may use regression equations to see if your data can indeed be fitted into a formula. If you want to create assumptions from your data, either future forecasts or indicators of previous behavior, using the Regression equation is highly beneficial.
The regression line is expressed as:
[tex]Y_i = a +bx_i[/tex]
where;
[tex]Y_i[/tex] = dependent variable
a = intercept
b = slope
[tex]x_i[/tex] = independent variable
So, when [tex]Y_i[/tex] is independent of the variation of [tex]x_i[/tex], it means that [tex]Y_i[/tex] does not linearly depend on [tex]x_i[/tex] . Thus, the slope of the regression will be zero.
Can I get help with this problem?
Answers
Answer:
4+1=5(0+1)
Step-by-step explanation:
The formula is y2-y1=slope(x2-x1)
Find the slope by using the formula y2-y1/x2-y1.
Out of 350 applicants for a job, 158 are female and 66 are female and have a graduate degree. Step 2 of 2 : If 110 of the applicants have graduate degrees, what is the probability that a randomly chosen applicant is female, given that the applicant has a graduate degree
Answers
Answer:
33/55
Step-by-step explanation:
Total applicants, n(T) = 350
Female applicants, n(F) = 158
Female and Graduate applicants, n(FnG) = 66
Graduates, n(G) = 110
Probability of female Given that applicant has graduate degree; this is a conditional probability problem;
Recall :
P(A given B) = P(A|B) = P(AnB) / P(B)
Therefore ;
P(F|G) = P(FnG) / P(G) = 66 / 110 = 33/55
Please answer these questions:
solve and simplify:
2/5 divided by 7/8
solve and simplify:
3/4 divided by 6/5
solve and simplify:
3/5 divided by 7/8
solve and simplify:
3/4 divided by 5/6
Answers
Answer
1• 2/5÷7/8
if there is a division sign in between two fractions what u have to do is multiply and, the fraction at the right need to change
=2/5×8/7
=16/35
=0•457
2• 3/4÷6/5
=3/4×5/618/24=0.753• 3/5÷7/8
=3/5×8/7
=24/35
=0•6857
4• 3/4÷5/6
=3/4×6/5
=18/20
=0•9
12.
What is the
equation of a circle with center (-7, -3) and radius 2?
Answers
Answer:
(x + 7)^2 + (y + 3)^2 = 4
Step-by-step explanation:
The standard equation of a circle is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center and r is the radius. We can substitute the information given to obtain:
(x + 7)^2 + (y + 3)^2 = 4
Can please send answers with step
Answers
Answer:
A. 14 Sq.cm
Step-by-step explanation:
The area of the circle is 56 cm Sq.
Half of it is 28 Sq.cm
If you combine the 2 triangles it will make an area of 7sq.cm
then the Curved shaded part is also 7sq.cm together of the shaded part will create a quarter of the whole figure
So
56/4 Sq.cm
= 14Sq.cm
Thank you!!
Mark me as brainliest :>>>
pls i need this one n i pass the class pls pls help me
Answers
9514 1404 393
Answer:
x = 5
Step-by-step explanation:
The two triangles are similar by the ASA theorem. The ratio of long side to short side in each right triangle is the same:
x/3 = 7.5/4.5
x = 3(7.5/4.5) . . . . multiply by 3
x = 5
If a(x) = 3x + 1 and (x)= x-4, what is the domain of (boa)(x)?
Answers
Answer:
[tex](b\circ a)(x)=3x-3[/tex] ; the domain is all real numbers
Step-by-step explanation:
[tex]a(x) = 3x+1[/tex]
[tex]b(x)=x-4[/tex]
[tex](b\circ a)(x)=b(a(x))=b(3x+1)=(3x+1)-4=3x+1-4=3x-3[/tex]
Therefore, the domain of the composite function is all real numbers.
solve the equation
x + -18 = 3x + 54
Answers
Answer:
-36
Step-by-step explanation:
See image below:)
Answer:
x = -36
Step-by-step explanation:
subtract 'x' from each side to get:
-18 = 2x + 54
subtract 54 from each side to get:
-72 = 2x
x = -72/2
x = -36
Suppose the mean percentage in Algebra 2B is 70% and the standard deviation is 8% What percentage of students pass the class with an 86% or better? Enter the value of the percentage without the percent sign.
Answers
Answer:
Z-value is what we called the number of standard deviations from the mean. 62% is 8% one standard deviation to the left, or a Z-value of -1. 94 is 24% to the right of the mean, or 3 standard deviations for a z-value of three. You can look on a Z-table to find the area between -1 and 3, which is .840 or 84%
Step-by-step explanation:
Please mark me as brainlist
If PQ = 4i+3j+2k, find /PQ/
Answers
Answer:
| PQ | = [tex]\sqrt{29}[/tex]
Step-by-step explanation:
Given
PQ = ai + bj + ck , then
| PQ | = [tex]\sqrt{a^2+b^2+c^2}[/tex]
Here PQ = 4i + 3j + 2k , then
| PQ | = [tex]\sqrt{4^2+3^2+2^2}[/tex] = [tex]\sqrt{16+9+4}[/tex] = [tex]\sqrt{29}[/tex]
Can y’all help me on question 26?!
Answers
Answer:
im pretty sure the answer is D. let me kno if im right
the result of subtraction of 3x from -4x is
Answers
Answer:
-x
Step-by-step explanation:
3x-4x= -x
The answer is minus x
hopes it helps
Answer:
-1x
Step-by-step explanation:
3x from &4x
= -4x-3x (minus minus =plus)
= 1x
Find missing number from letter n ! Please
Answers
Answer:
1. n= 20 /13
2. n=10
3. n=35
4. n=9
That's all I could do, I got tired of typing lol
Step-by-step explanation:
1. 4/n=13/5 we cross multiply, (4)*(5)=13*n, 20=13n Flip the equation. 13n=20, divide 13 on both sides, 13n/13=20/13, n= 20 /13
2. 9/6= 15/n, we cross multiply 9*n=(15)*(6), 9n=90, Divide both sides by 9. 9n/9=90/9 n=10
3. 28/4=n/5 Cross-multiply, (28)*(5)=n*(4), 140=4n Flip the equation.4n=140 Divide both sides by 4. 4n/4=140/4 n=35
4. n/6=6/4 we cross multiply,n*(4)=(6)*(6), 4n=36, Divide both sides by 4 4n/4=36/4. n=9
A square with sides x ft long has a
perimeter of 343 ft. How long are the
sides of the square?
Answers
The perimeters formula is
4L where L is the length of the side
Now 343 = 4L
343/4=x
So x =85.75
I hope you understand: )
What is the value of log
?
1/100
Answers
I hope this is gelpful for u