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.