Korey and Lauren decided they needed to see their local bank to check on their accounts.

Korey thinks that they should deposit $500 for the initial amount. This account has a 3% interest rate that is compounded quarterly.

Lauren thinks that they should deposit $500 for the initial amount. This account has a 4% interest rate that is compounded monthly.

Who's idea will really pay off? Which method would be the best for having more money after leaving the money untouched for 2 years.

Lauren's method would be the best for having more money after leaving the initial deposit untouched for 2 years.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Initial amount = $ 500

Korey's interest rate = 3% compounded quarterly = 0.03/4

Lauren's interest rate = 4% compounded monthly = 0.04/12

2. Who's idea will really pay off? Which method would be the best for having more money after leaving the money untouched for 2 years.

Let's use the compound interest formula this way:

A = P * (1 + r/n) ⁿˣ, where:

A = final balance of the account

P = initial deposit ($ 250)

r = interest rate  (0.03/4 or 0.04/12)

n = number of times interest applied per time period (4 quarters or 12 months)

x = number of time periods elapsed (2 years)

Now we can calculate Korey's method this way:

A = 500 * (1 + 0.03/4)⁴°²

A = 500 * (1.0075)⁸

A = 500 * 1.061598848

A = $ 530.80 (Rounding to the next cent)

Now we can calculate Lauren's method this way:

A = 500 * (1 + 0.04/12)¹²°²

A = 500 * (1.0033)²⁴

A = 500 * 1.083142959

A = $ 541.57 (Rounding to the next cent)

Lauren's method would be the best for having more money after leaving the initial deposit untouched for 2 years.

(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:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

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