The formula used to calculate the value of a savings accounty =(1+)120What does theafter t years is A(t)=0.04= 1500 1+120.04frac
tion represent?12y=a(1)aeAthe daily interest rateB how long the money has been in the accountCthe monthly interest rateD the starting balance in the account
1 answer:
We have here the formula for Compound Interest:
Where:
• A is the accrued amount.
,• P is the Principal (the original amount of money, the starting amount of money).
,• r is the interest rate.
,• n is the number of times per year compounded.
,• t is the time in years.
When we have that n is equal to 12, we are talking here about that the amount of money is being compounded monthly (we have 12 months in a year, 12 periods, n = 12). <em>Therefore, we are dividing the rate, r, by the number of compoundings per year, n, and this is the rate per each new compounding period of time, r/n, and, in this case, n = 12 (monthly interest rate). </em>
Therefore, in few words, the fraction (0.04/12) is the monthly interest rate (option C).
[If we see the other options, we have:
• The daily interest rate would be given by 0.04/365.
,• How long the money has been in the account is time, t.
,• The starting balance in the account is the Principal, P. ]
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Answer:
M = (8,9)
Step-by-step explanation:
Notice that the points (0,15), and (20,0) form with the origin of coordinates (0,0), a right angle triangle (please see attached image). This triangle has twon perpendicular sides of length 15 and 20 respectively. Therefore, we can find the length of the segment that joins points A (0,15) and B (20,0) by finding the length of the hypotenuse in a right angle triangle (with the Pythagorean Theorem):
Now, to get a 2:3 proportion on Segment AB which is of length 25, we need to divide it in five equal parts (see the picture on the right of the attached image), and place point M at two of these divisions from point A (0,15) and along segment AB.
In order to find the appropriate location in (x,y) coordinates, we consider a smaller triangle (pictured in orange in the image) that is similar to the first larger triangle (pictured in blue). Notice that if the length of AB is 25, each of its five equal divisions would be of length "5", and therefore two of them will render a length of "10" (which is the hypotenuse of this smaller right angle triangle.
Now, in order to find the sides of this smaller triangle (which can give us the clues on the horizontal and vertical coordinates of point M), we can use proportions.
To find the length "x" of the horizontal side , we do:
To find the length "y" of the vertical side , we do:
Then, the coordinate "x" of point M will be "8", while we can calculate the y position of point M subtracting "6" from 15 (the length of the vertical side in the original triangle). This gives us the coordinates (8,9) for point M as marked in orange in the picture.
