Mathematics, 25.07.2019 22:30 Serenitybella

Dempsey transferred a balance of $5600 to a new credit card at the beginning of the year. the card offered an introductory apr of 6.6% for the first 4 months and a standard apr of 24.8% thereafter. if the card compounds interest monthly, what will dempsey's balance be at the end of the year? (assume that dempsey will make no payments or new purchases during the year, and ignore any possible late payment fees.) a. $6741.98 b. $6595.68 c. $5724.22 d. $7158.06

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Answer from: GamerGirl15

The correct option is A. $6741.98

Step-by-step explanation:

Principal value = $5600

Rate of interest for 4 months = 6.6%

n = 12

Time = 4 months

$\text{Compound Interest = }Principal\times (1+\frac{Rate}{100\times n})^{n\times Time}\\\\\implies \text{Compound Interest = }5600\times (1+\frac{6.6}{100\times 12})^{12\times \frac{4}{12}}\\\\\implies \text{Compound Interest = }5600\times (1+\frac{6.6}{100\times 12})^{4}\\\\\implies \text{Compound Interest = }\$5724.22$

Now, Principal = $5724.22

Time = 8 months

Rate of interest = 24.8

$\text{Compound Interest = }Principal\times (1+\frac{Rate}{100\times n})^{n\times Time}\\\\\implies \text{Compound Interest = }5724.22\times (1+\frac{24.8}{100\times 12})^{12\times \frac{8}{12}}\\\\\implies \text{Compound Interest = }5724.22\times (1+\frac{24.8}{100\times 12})^{8}\\\\\implies \text{Compound Interest = }\$6741.98$

Hence, The correct option is A. $6741.98

Answer from: Quest

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step-by-step explanation:

Answer from: Quest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2: