Suppose that a family wants to start a college fund for their child. If they can get a rate of 5.5% , compounded monthly, and want the fund to have a value of $35,450 after 20 years, how much should they deposit monthly? Assume an ordinary annuity and round to the nearest cent.
Answers
Answer:
They should deposit $81.38 monthly.
Step-by-step explanation:
We know that,
where,
FV of annuity = $35,450
P = monthly payment,
r = rate of interest = 5.5% annually =
n = number period = 20 years = 240 months
Putting all the values,
Therefore, they should deposit $81.38 monthly.
=> 12 * 20 = 240 months
=> 35 450 / 240 months = 147.7 dollars per month is the money with interest
Let's subtract the interest
=> 147.7 * 0.055 = 8.1 dollars.
=> 147.7 - 8.1 = 139.6 dollars per month.
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Answer C (-3,2)
1.) What is the sum of the interior angles of a polygon having 8 sides?
2.) Find the measure of the exterior angle of a regular decagon.
3.) Find the number of diagonals of a nonagon.
4.) What is the measure of each angle of a regular nonagon?
5.) if the sum of the measures of the angles of a regular polygon is 900, then
what is the number of sides?
Answers
Answer:
1. 1080°
2. 36°
3. 27 diagonals
4. 140°
5. 7 sides
Step-by-step explanation:
1. The sum S of the interior angles of a polygon is given by;
S = (n-2) x 180°
Where;
n = number of sides of the polygon.
Therefore, to get the sum of the interior angles of a polygon having 8 sides, we substitute n = 8 into equation (i) as follows;
S = (8 - 2) x 180°
S = 6 x 180°
S = 1080°
Therefore, the sum of the interior angles of a polygon having 8 sides is 1080°
2. The sum of interior angles of a polygon is given by;
S = (n - 2) x 180°
For a polygon which is a regular decagon where the number of sides n = 10, the sum is;
S = (10 - 2) x 180°
S = 8 x 180°
S = 1440°
Since the decagon is regular, then each of its interior angles is given by;
1440° / 10
=> 144°
Now, since we know that the sum of the interior angle and exterior angle will give 180°, then;
The exterior angle of a regular decagon is;
180° - 144° = 36°
Therefore, the exterior angle of a regular decagon is 36°
3. The number of diagonals N of a polygon with n sides is given by;
N =
So, for a nonagon which has 9 sides (i.e n = 9), the number of diagonals is;
N =
N =
N = 9(3)
N = 27
Therefore, a nonagon has 27 diagonals.
4. The sum of interior angles of a polygon is given by;
S = (n - 2) x 180°
For a polygon which is a nonagon where the number of sides n = 9, the sum is;
S = (9 - 2) x 180°
S = 7 x 180°
S = 1260°
Since the nonagon is regular, then each of its interior angles is given by;
1260° / 9
=> 140°
Therefore, the measure of each angle (interior angle) of a regular nonagon is 140°
5. The sum of the interior angles of a polygon is given by;
S = (n - 2) x 180°
So if the sum is 900, then to get the number of sides of the polygon, we substitute S = 900 into the equation;
900° = (n - 2) x 180°
Divide through by 180°
5 = (n - 2)
Solve for n;
n = 5 + 2
n = 7
Therefore, the regular polygon has 7 sides.
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Or you can use
A is equal to 45 million
To find the rate, k, we can plug in:
Knowing that t = 4
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A triangle is 180°. So you can do:
3.2n + 6.4n + 2.4n = 180 Simplify
12n = 180
n = 15 Now that you know the value of n, you can plug it into each individual angle/equation
∠X = 3.2n plug in 15 for n
∠X = 3.2(15)
∠X = 48°
∠Y = 6.4(15)
∠Y = 96°
∠Z = 2.4(15)
∠Z = 36°