This is specifically for chika
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Answer:
Decide the length of your investment period. If it is 12 years or longer, then the account earning compound interest will pay more.
Step-by-step explanation:
The account balance (A) in the simple interest account will be the principal amount (P) added to the interest earned.
A = P + P·0.05·t = P(1+.05t)
Assuming the interest is compounded annually, the account balance in the compound interest account will be the principal amount multiplied by the factor representing the growth due to interest.
A = P(1 +0.04)^t = P·1.04^t
After some number of years, the second account balance will exceed the first account balance. That number of years cannot be found algebraically, but it can be found by graphing or by trial-and-error. It can be found to be about 11.919 years, or about 11 years and 11 months.
If interest is compounded more often than once per year, the break-even point will shorten slightly. It will never be shorter than 10.77 years (compounded continuously).
Answer:
Step-by-step explanation:
We have the system of equations:
We can convert this to a matrix. In order to convert a triple system of equations to matrix, we can use the following format:
Importantly, make sure the coefficients of each variable align vertically, and that each equation aligns horizontally.
In order to solve this matrix and the system, we will have to convert this to the reduced row-echelon form, namely:
Where the (x, y, z) is our solution set.
Reducing:
With our system, we will have the following matrix:
What we should begin by doing is too see how we can change each row to the reduced-form.
Notice that R₁ and R₂ are rather similar. In fact, we can cancel out the 1s in R₂. To do so, we can add R₂ to -2(R₁). This gives us:
Now, we can multiply R₂ by -1/5. This yields:
From here, we can eliminate the 3 in R₃ by adding it to -3(R₁). This yields:
We can eliminate the -5 in R₃ by adding 5(R₂). This yields:
We can now reduce R₃ by multiply it by -1/4:
Finally, we just have to reduce R₁. Let's eliminate the 2 first. We can do that by adding -2(R₂). So:
And finally, we can eliminate the second 1 by adding -(R₃):
Therefore, our solution set is
And we're done!