114/2=57 I believe 57 is the correct answer
Answer:
Step-by-step explanation:
9(y = 1/9x + 5)
9y = x + 45
-x + 9y = 45
x - 9y = -45
The rotation that that translates AWXY to AW'X'Y' is a 45° anticlockwise rotation. See the attached image for details.
<h3>What is a rotation in math?</h3>
Rotation in math refers to the change in the angle of a geometric shape around a central axis on a point on the geometric plane such that it's original coordinates are modified but it's size or shape.
Hence, it is correct to state that The rotation that that translates AWXY to AW'X'Y' is a 45° anticlockwise rotation.
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The amount to be invested today so as to have $12,500 in 12 years is $6,480.37.
The amount that would be in my account in 13 years is $44,707.37.
The amount I need to deposit now is $546.64.
<h3>How much should be invested today?</h3>
The amount to be invested today = future value / (1 + r)^nm
Where:
- r = interest rate = 5.5 / 365 = 0.015%
- m = number of compounding = 365
- n = number of years = 12
12500 / (1.00015)^(12 x 365) = $6,480.37
<h3>What is the future value of the account at the end of 13 years?</h3>
Future value = monthly deposits x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
- r = interest rate = 5.3 / 12 = 0.44%
- n = 13 x 12 = 156
200 x [{(1.0044^156) - 1} / 0.0044] = $44,707.37
<h3>What should be the monthly deposit?</h3>
Monthly deposit = future value / annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
- r = 6.7 / 12 = 0.56%
- n = 2 x 12 = 24
$14,000 / [{(1.0056^24) - 1} / 0.0056] = $546.64
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