Use the compound interest formula to find the compound amount on a $12,000 investment at 5% compounded quarterly for 4 years.
1 answer:
Total = Principal * [1 + (rate/n)]^n*years
Where "n" is the compounding periods per year
Total = 12,000 * (1+(.05/4))^(4*4)
Total = 12,000 * (1.0125)^(16)
Total = 12,000 * <span> <span> <span> 1.2198895477 </span> </span> </span> <span> </span>
Total = <span> <span> </span></span><span><span><span>14,638.67</span>
</span> </span>
Where "n" is the compounding periods per year
Total = 12,000 * (1+(.05/4))^(4*4)
Total = 12,000 * (1.0125)^(16)
Total = 12,000 * <span> <span> <span> 1.2198895477 </span> </span> </span> <span> </span>
Total = <span> <span> </span></span><span><span><span>14,638.67</span>
</span> </span>
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We will investigate how to determine Hamilton paths and circuits
Hamilton path: A path that connect each vertex/point once without repetition of a point/vertex. However, the starting and ending point/vertex can be different.
Hamilton circuit: A path that connect each vertex/point once without repetition of a point/vertex. However, the starting and ending point/vertex must be the same!
As the starting point we can choose any of the points. We will choose point ( F ) and trace a path as follows:
The above path covers all the vertices/points with the starting and ending point/vertex to be ( F ). Such a path is called a Hamilton circuit per definition.
We will choose a different point now. Lets choose ( E ) as our starting point and trace the path as follows:
The above path covers all the vertices/points with the starting and ending point/vertex are different with be ( E ) and ( C ), respectively. Such a path is called a Hamilton path per definition.
One more thing to note is that all Hamilton circuits can be converted into a Hamilton path like follows:
The above path is a hamilton path that can be formed from the Hamilton circuit example.
But its not necessary for all Hamilton paths to form a Hamilton circuit! Unfortunately, this is not the case in the network given. Every point is in a closed loop i.e there is no loose end/vertex that is not connected by any other vertex.