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Sonja [21]
3 years ago
13

Find the value of annuity if the periodic deposit is $400 at 4% compounded monthly for 18 years

Mathematics
1 answer:
vlada-n [284]3 years ago
6 0

Answer:

~820.8$

Step-by-step explanation:

The total money (M) after 18 years could be calculated by:

M = principal x (1 + rate)^time

with

principal = 400$

rate = 4% compounded monthly = 0.04/12

time = 18 years = 18 x 12 = 216 months (because of compounded monthly rate)

=> M = 400 x (1 + 0.04/12)^216 = ~820.8$

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What is the product?
Wewaii [24]

Answer:

-30a^5b + 12a^4b^3 + 16a^3b^2 - 4a^2b^4 - 2 ab^3

Step-by-step explanation:

6 0
2 years ago
The average THC content of marijuana sold on the street is 9.3%. Suppose the THC content is normally distributed with standard d
velikii [3]

Answer:

a) X \sim N(9.3,1)  

b) P(X>9.2)=P(\frac{X-\mu}{\sigma}>\frac{9.2-\mu}{\sigma})=P(Z>\frac{9.2-9.3}{1})=1-P(Z

c) The value of height that separates the bottom 75% of data from the top 25% is 9.9745.  

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

2) Part a

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

X \sim N(9.3,1)  

Where \mu=9.3 and \sigma=1

3) Part b

We are interested on this probability

P(X>9.2)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>9.2)=P(\frac{X-\mu}{\sigma}>\frac{9.2-\mu}{\sigma})=P(Z>\frac{9.2-9.3}{1})=1-P(Z

4) Part c

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.25   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.6745. On this case P(Z<0.6745)=0.75 and P(z>0.6745)=0.25

If we use condition (b) from previous we have this:

P(X  

P(Z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.6745

And if we solve for a we got

a=9.3 +1*0.6745=9.9745

So the value of height that separates the bottom 75% of data from the top 25% is 9.9745.  

8 0
3 years ago
this month salespersons a made 11% of $67,530. salesperson b made 8% of $85,740. who made more commission this month? how much d
Paul [167]
Salesperson A made $7428.30
Salesperson B made $6859.20
Salesperson A made more commission this month and made $7428.30
7 0
3 years ago
Read 2 more answers
Leo has a lock box with a volume of 312 cubic inches. The box is 4 inches high and 13 inches long. What is the width of the box?
natima [27]

Answer:

6in

Step-by-step explanation:

Given data

Volume of the lockbox= 312 cubic inches

Height= 4in

Length= 13in

Width= ???

The expression for the volume of box is

V= L*W*H

substitute

312=13*W*4

312=52W

W= 312/52

W=6 in

Hence the width is 6in

6 0
3 years ago
. An elevator starts at the 6th floor. It goes up 7 floors twice, and then it goes
Anettt [7]

Well let's see what floor each one lands on and figure out which one is higher.

Something to note:

down = subtracting

up = adding

if something says it's doing something more than once, add it the number of times it's doing that thing. (You can also multiply it by that number but the adding way is a bit easier to understand and explain)

<u>Elevator 1:</u>

6 + 7 + 7 - 10 = 10

<u>Elevator 2:</u>

20 - 5 - 5 - 5 + 12 = 17

Elevator 2 ends on a higher floor (reasoning above)

4 0
3 years ago
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