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11111nata11111 [884]

3 years ago

10

Jay Field’s bank granted him a single-payment loan of $6,800. He wanted to compare repaying the loan in 91 days at an ordinary i

nterest rate of 4.25% to repaying the loan in 91 days at an exact interest rate of 4.23%. Which interest rate is a better deal for Jay? How much does he save?

2 answers:

Aleksandr-060686 [28]3 years ago

8 0

Answer:

Amount of loan = $6800

Time period = 91 days

When interest rate is 4.25%

$Amount = 6800\times(1+\frac{4.25}{12\times 100})^{12\times\frac{91}{30\times 12}}\\\\Amount=\$6873.32$

When interest rate is 4.23%

$Amount = 6800\times(1+\frac{4.23}{12\times 100})^{12\times\frac{91}{30\times 12}}\\\\Amount=\$6872.96$

So, the amount paid with 4.23% interest rate is less

Hence, 4.23% interest rate is a better deal for Jay.

Amount saved = 6873.32 - 6872.96

= $0.36

ArbitrLikvidat [17]3 years ago

6 0

I don't know if you still need help with this, but the answer is exact interest and he saves $1.34.

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2 years ago

Which of the following functions are homomorphisms?

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Part A:

Given $f:Z \rightarrow Z,$ defined by $f(x)=-x$

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Part B:

Given $f:Z_2 \rightarrow Z_2,$ defined by $f(x)=-x$

Note that in $Z_2$ , -1 = 1 and f(0) = 0 and f(1) = -1 = 1, so we can also use the formular $f(x)=x$

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and

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Part C:

Given $g:Q\rightarrow Q$ , defined by $g(x)= \frac{1}{x^2+1}$

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Since, f(x+y) ≠ f(x) + f(y), therefore, the function is not a homomorphism.

Part D:

Given $h:R\rightarrow M(R)$ , defined by $h(a)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)$

$h(a+b)= \left(\begin{array}{cc}-(a+b)&0\\a+b&0\end{array}\right)= \left(\begin{array}{cc}-a-b&0\\a+b&0\end{array}\right) \\ \\ h(a)+h(b)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)+ \left(\begin{array}{cc}-b&0\\b&0\end{array}\right)=\left(\begin{array}{cc}-a-b&0\\a+b&0\end{array}\right)$

but

$h(ab)= \left(\begin{array}{cc}-ab&0\\ab&0\end{array}\right) \\ \\ h(a)\cdot h(b)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)\cdot \left(\begin{array}{cc}-b&0\\b&0\end{array}\right)= \left(\begin{array}{cc}ab&0\\-ab&0\end{array}\right)$

Since, h(ab) ≠ h(a)h(b), therefore, the funtion is not a homomorphism.

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Then, for any $[a_{12}],[b_{12}]\in Z_{12}$ , we have

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$f\left([a_{12}][b_{12}]\right)=f\left([ab]_{12}\right) \\ \\ =[ab]_4=[a]_4[b]_4=f\left([a]_{12}\right)f\left([b]_{12}\right)$

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Answer: The number is 1.

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2 years ago