The Rule of 72 is a shortcut method to find the number of years to double your investment. This is only an estimation. This can be done by dividing 72 by the annual interest rate.
However, you are given a nominal rate since it is compounded annually. Let's convert this by this equation:
annual rate = (1+i/m)^m - 1, where m is the number of periods in a year. Thus, m=2
annual rate = (1 + 0.065/2)^2 -1 = 6.61%
Applying Rule of 72,
72 ÷ 6.61% = 10.89
This is where I found a problem. The answer here just directly divided 72 by 6.5% which will equal to 11.1 years. This is not accurate, since the given interest is compounded semi-annually. That is not an annual interest rate.
Nevertheless, the answer is still close to letter A.) 11.1 years.
Answer:
(2,0) - x -intercept
(0, 1.5) - y-intercept
Step-by-step explanation:
The slope of the points can be found by writing a ratio of vertical change to horizontal change. It can be found in the table by subtracting y values from each other and subtracting x values from each other. The y values decrease by 3 each time or -6 - -3 = -6 + 3 = -3.
The x values increase by 4.
So the rate of change is -3/4.
This means if you go backwards on the table the previous point would be (2, 0). This is the x-intercept.
To find the y-intercept, you must go further back. Going back 2 more units would make the table appear as:
x y
-2 3
0 ???
2 0
6 -3
10 -6
14 -9
Since the y values decrease by 3 each time and we went back half the usual amount, then the value would be 1.5.
Answer:
Slope = -1/2
Y-Intercept = 2
Equation: Y=-1/2x+2
Step-by-step explanation:
Graph goes 2 units up at y=2, that's your y-intercept. From there, plot your second point by moving 1 down and 2 to the right from the y-intercept, landing on the point (2,1) to get your slope, written as -1/2.
