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2 years ago

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Say you are considering two loans. Loan F has a nominal interest rate of 5. 66%, compounded monthly. Loan G has a rate of 6. 02%

, compounded semiannually. Which loan will give the lower effective interest rate, and how much lower will it be? a. Loan Gâ€™s effective rate will be 0. 091 percentage points lower than Loan Fâ€™s. B. Loan Gâ€™s effective rate will be 0. 058 percentage points lower than Loan Fâ€™s. C. Loan Fâ€™s effective rate will be 0. 302 percentage points lower than Loan Gâ€™s. D. Loan Fâ€™s effective rate will be 0. 149 percentage points lower than Loan Gâ€™s.

1 answer:

kompoz [17]2 years ago

6 0

Option C: Loan F's effective rate will be 0.302 percentage points lower than Loan G's.

<h2>Given that:</h2>

For loan F: Interest rate is 5.66% compounding monthly.

For loan G: Interest rate is 6.02% compounded semi-annually.

<h2>Calculations:</h2>

Effective rate for loan F will be calculated as:

$r = (1 + \dfrac{0.0566}{12})^{12} - 1 \: \: ; n = 12\\or\\r = 0.0580916$

Effective rate for loan G:

$r = (1 + \dfrac{0.0602}{2})^{2} - 1 \: \: ; n = 2\\or\\r = 0.061106$

Thus the difference between effective rate of loan G from that of loan F is

$= 0.061106 - 0.058091\\\approx 0.00302\\or\\0.00302 \times 100 \: percent\\\\= 0.302 \: percent$

Thus option C is correct.

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brainly.com/question/25857212

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Drag the tiles to the boxes to form correct pairs.<br> Match the pairs of equivalent expressions.

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Answer:

The following pairs/results are matched:

$5\left(2t+1\right)+\left(-7t+28\right)$ = $3t+33$
$3\left(3t-4\right)-\left(2t+10\right)$ = $7t-22$

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Step-by-step explanation:

Lets solve all the expressions to match the results.

$5\left(2t+1\right)+\left(-7t+28\right)$

<em>Solving the expression</em>

$5\left(2t+1\right)+\left(-7t+28\right)$

$\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a$

$5\left(2t+1\right)-7t+28$

$10t+5-7t+28$

$3t+33$

Therefore, $5\left(2t+1\right)+\left(-7t+28\right)$ = $3t+33$

$3\left(3t-4\right)-\left(2t+10\right)$

<em>Solving the expression</em>

$3\left(3t-4\right)-\left(2t+10\right)$

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$9t-12-2t-10$

$7t-22$

Therefore, $3\left(3t-4\right)-\left(2t+10\right)$ = $7t-22$

$\left(4t-\frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)$

<em>Solving the expression</em>

$\left(4t-\frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$4t-\frac{8}{5}-\left(3-\frac{4}{3}t\right)$

$4t-\frac{8}{5}-\left(-\frac{4t}{3}+3\right)$

$4t-\frac{8}{5}-3+\frac{4t}{3}$

As

$-3-\frac{8}{5}:\quad -\frac{23}{5}$ and $\frac{4t}{3}+4t:\quad \frac{16t}{3}$

So,

$4t-\frac{8}{5}-3+\frac{4t}{3}$ will become $\frac{16t}{3}-\frac{23}{5}$

Therefore, $\left(4t-\frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)$ = $\frac{16t}{3}-\frac{23}{5}$

$\left(-\frac{9}{2}t+3\right)+\left(\frac{7}{4}t+33\right)$

<em>Solving the expression</em>

$\left(-\frac{9}{2}t+3\right)+\left(\frac{7}{4}t+33\right)$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$-\frac{9}{2}t+3+\frac{7}{4}t+33$

$\mathrm{Group\:like\:terms}$

$\frac{9}{2}t+\frac{7}{4}t+3+33$

$\mathrm{Add\:similar\:elements:}\:-\frac{9}{2}t+\frac{7}{4}t=-\frac{11}{4}t$

$-\frac{11}{4}t+3+33$

$-\frac{11}{4}t+36$

Therefore, $\left(-\frac{9}{2}t+3\right)+\left(\frac{7}{4}t+33\right)$ = $-\frac{11}{4}t+36$

Thus, the following pairs/results are matched:

$5\left(2t+1\right)+\left(-7t+28\right)$ = $3t+33$
$3\left(3t-4\right)-\left(2t+10\right)$ = $7t-22$

$\left(4t-\frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)$ = $\frac{16t}{3}-\frac{23}{5}$

$\left(-\frac{9}{2}t+3\right)+\left(\frac{7}{4}t+33\right)$ = $-\frac{11}{4}t+36$

Keywords: algebraic expression

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3 years ago

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