What's the present value of $11,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually?
General Idea:
We need to make use of the below formula to find the present value.
[tex] PV=\frac{FV}{(1+\frac{r}{n})^{nt}} \\ \\ Where:\\ FV \; is \; Future\; Value\; of \; money\\ r \; is\; Annual\; rate\; of\; interest\\ t\; is\; number\; of\; years\\ n\; is\; Number\; of\; periods\; based\; on\; compounding \; frequency [/tex]
Applying the Concept:
We are given the below information:
[tex] FV= \$11,500\\ \\ t=5\; years\\ \\ r=4.5 \%\\ \\ n=2\; (because\; given\; compounded\; semi-annually) [/tex]
We need to substitute the above information in the formula to find the Present value.
[tex] PV=\frac{11500}{(1+\frac{0.045}{2})^{2 \times 5}} =\frac{11500}{(1+0.0225)^{10}} =\frac{11500}{1.0225^{10}} \\ \\ PV \approx \$9206 [/tex]
CONCLUSION:
The present value of $11,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually is approximately 9206 dollars
Factor.x ^2 + 17x + 72
Find factors of x^2 and 72, that, when combined, will give you 17x
x ^2 + 17x + 72
x 9
x 8
(x + 9)(x + 8) is your factor.
hope this helps
the value of the building owned by two veterinarians went from 125000 to 117500. What is the percent decrease
Please help me with question 26
What has an infinite number of points extending in opposite directions that has only one dimension
A magazine claims that 75% of all teenage boys have their own cellphones. A researcher wished to test the claim and selected a random sample of 60 teenage boys. She found that 54 had their own cell phones. At α = 0.01, should the claim be rejected?
A student is raising money for a homeless shelter. A local business agrees to donate an additional 20% of what the student raises, while a local politician also agrees to donate an additional 10% of what the student raises. If the student raises $600.00, how much will be donated?
Answer: the answer is $780.00
Step-by-step explanation:
$600.00 x .20 = $120.00
$600.00 x .10 = $60.00
Total:
$600.00 + $120.00 + $60.00 = $780.00
Answer:
780
Step-by-step explanation:
Factor each expression: 5a-25
Find the reference angle for 697 degrees
A website is offering a promotion, during which customers can buy up to 100 photos for a flat fee. The cost per photo varies inversely with the number of photos a customer buys, as shown in the table below. What functions model the data?
Your answer is nc=100
The length of time that an auditor spends reviewing an invoice is approximately normally distributed with a mean of 600 seconds and a standard deviation of 100 seconds. what is the probability that an auditor will spend more than 12 minutes on an invoice?
The probability that an auditor will spend more than 12 minutes on an invoice is approximately 88.49%.
Calculate the probability an auditor will spend more than 12 minutes on an invoice using the Z-score formula for a normal distribution.
The probability that an auditor will spend more than 12 minutes on an invoice can be calculated using the Z-score formula for a normal distribution.
Calculate the Z-score: Z = (12*60 - 600) / 100 = -1.2.Find the probability corresponding to this Z-score using a standard normal distribution table. P(Z > -1.2) = 0.8849.Therefore, the probability that an auditor will spend more than 12 minutes on an invoice is approximately 88.49%.the price of a tablet was reduced from $250 to $200. By what percentage was the price of the tablet reduced? Please help me solve this.
(Multiple Choice Worth 4 points) (05.01)A flower bed is in the shape of a triangle, with a base of 13 feet and a height of 5 feet. What is the area of the flower bed?
A 18 square feet
B 32.5 square feet
C 65 square feet
D 130.5 square feet
Answer:
b
Step-by-step explanation:
In a multiple regression analysis what would likely be the culprit of a dramatic increase in the P-value of one of the variables?
a total of 324 tickets were sold for the school play they were either adult tickets or student tickets the number of student tickets sold was three times the number of adults tickets sold how many adult tickets were sold?
The correct answer is 81
Final answer:
To find the number of adult tickets sold when a total of 324 tickets were sold for a school play and student tickets were three times the number of adult tickets, we set up the equation x + 3x = 324, solved for x, and found out that 81 adult tickets were sold.
Explanation:
The question is asking us to find out how many adult tickets were sold when a total of 324 tickets were sold for a school play, with the number of student tickets being three times the number of adult tickets sold. To solve this, we let x represent the number of adult tickets. Therefore, 3x will represent the number of student tickets since there are three times as many student tickets as adult tickets.
The equation representing the total number of tickets sold would be: x (adult tickets) + 3x (student tickets) = 324. Simplifying, we have 4x = 324. Dividing both sides by 4 gives us x = 81.
Therefore, the number of adult tickets sold is 81.
Angle D is a vertical angle to F. The measure of D is 53° . What is the measure of F?
Angle F will have the same measure as angle D, which is 53°, because they are vertical angles and thus congruent.
Explanation:The question asks about the measure of angle F given that it is a vertical angle to angle D, which measures 53°. In geometry, vertical angles (also known as opposite angles) are pairs of non-adjacent angles formed when two lines intersect. Vertical angles are congruent, which means they have the same measure. Therefore, since angle D is 53°, angle F, being its vertical angle, will also have a measure of 53°.
Angle D and angle F are vertical angles, which means they are congruent. If angle D measures 53°, then angle F will also measure 53°. This is because vertical angles are equal in measure.
Finally, 43 is 5% of what number?
Use the simplified ratio to find the equivalent ratio with a numerator of 43.
Enter your answer in the box.
43 is 5% of __?
Final answer:
43 is 5% of 860.
Explanation:
To find out what number 43 is 5% of, we can set up a proportion where 5% (or 0.05 when written as a decimal) is equal to 43 over an unknown total number X.
The formula to calculate this is part = percentage imes total, which in this case turns into 43 = 0.05 * X.
To solve for X, divide 43 by 0.05, giving us X = 43 / 0.05 which equals 860.
Therefore, 43 is 5% of 860.
Your friend earns $10.50 per hour. This is 125% of her hourly wage last year. How much did your friend earn per hour last year?
Ms Cohen gave a riddle: A string is 2 meters longer than a rod. Half of the rod is 1 meter shorter than half of the string. Is this true or false?
You have 10 different video games. how many different ways can you arrange the games side by side on a shelf
You can arrange the games side by side on a shelf in "3628800" ways.
According to the question,
Number of video games,
10Now,
The amount of possible ways could you place the games side by side on some kind of shelf will be:
= [tex]10![/tex]
= [tex]10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1[/tex]
= [tex]3628800[/tex]
Thus the response above is appropriate.
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Where a is determined by the conditions x2 + y2 ≤ 1 and x + y ≥ 1?
Efetue as divisões X ao cubo+10x+29x+20:x ao quadrado+5x+4
If a salesperson sells 3/4 of an acre for $80,000, what was the price per square foot rounded to two decimal spaces?
Following are the calculation to the given question:
Given:
salesperson sells[tex]\bold{= \frac{3}{4}}[/tex]
acre= 80,000
To find:
price per square foot rounded to two decimal spaces=?
Solution:
Therefore
[tex]1 \ acre=43560\ foot \\\\ \frac{3}{4}\ acre=32670\ foot[/tex]
Calculation
[tex]32670 \ sq \ foot = \$80,000 \\\\1 \ sq \ foot =? \\\\[/tex]
Calculating the price:
[tex]=\frac{80,000}{32670}=2.4487 \approx 2.45[/tex]
Therefore, the final answer is "$2.45".
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Suppose you have two credit cards. The first has a balance of $410 and a credit limit of $1,000. The second has a balance of $510 and a credit limit of $1,000. What is your overall credit utilization? 36% 56% 46% 16% 26%
Could someone help me with this?
Create a pattern with the rule n x 2 + 1
The pattern that can be created with the rule n x 2 + 1 is 1, 3, 5, 7, 9, 11
Given:
n × 2 + 1
= 2n + 1
where
n = number of terms
when n = 0
2(0) + 1
0 + 1
= 1
when n = 1
2(1) + 1
= 2 + 1
= 3
when n = 2
2(2) + 1
4 + 1
= 5
when n = 3
2(3) + 1
6 + 1
= 7
when n = 4
2(4) + 1
8 + 1
= 9
Therefore, the pattern that can be created with the rule n x 2 + 1 is 1, 3, 5, 7, 9, 11
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Rhoads earned $324.65 delivering newspapers. She promised her sister 0.2 of her earnings for helping her.How much does Rhoads owe her sister?
Do I have to subtract?? if not help me solve plz
which of the following shows an equivalent expression to (5 times 3)times 12 if only associative property was used to transform the expression
⇒Associative Property states
A × (B ×C)=(A×B)×C=(A×C)×B
Now, we have to find equivalent expression of
[tex](5 \times 3) \times 12 \\\\1.\rightarrow 5 \times (3 \times 12)\\\\2.\rightarrow (5 \times 12) \times 3\\\\3 \rightarrow 180[/tex]
what is the coefficient of the term 13a in the expression 13a+6b
I need help !! This packet is due tomorrow and I have no idea what I’m doing .
Answer:
Given is :
∠M≅∠X
∠N≅∠Y
YO≅NZ
We have to prove that ΔMNO≅ΔXYZ
Using segment addition postulate we get YZ=YO+OZ and ON=NZ+OZ and YO=NZ is already given. Using substitution of YO for NZ; we get ON=YO+OZ
Now substituting YZ for YO+OZ we get ON=YZ and also YZ=YO+OZ.
Now applying AAS we get ΔMNO is congruent to ΔXYZ because of angle-angle-side theorem as we have already proved that two sides are congruent and a non-included angle in each triangle is congruent.