Algebra 2 help!

Question

Patrick and Brooklyn are making decisions about their bank accounts. Patrick wants to deposit $300 as a principal amount, with an interest of 3% compounded quarterly. Brooklyn wants to deposit $300 as the principal amount, with an interest of 5% compounded monthly. Explain which method results in more money after 2 years.

Answer 1

To compare the two methods, we need to calculate the total amount of money each person will have after 2 years.

For Patrick, we use the formula for compound interest: A = P (1 + r/n)^(nt) where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

So, A = 300 (1 + 0.03/4)^(42) = 300 (1.0075)^8 = 3001.2456 = $372.68

For Brooklyn, we use the same formula but with a different interest rate and number of times compounded per year.

A = 300 (1 + 0.05/12)^(122) = 300 (1.004167)^24 = 3001.0888 = $326.64

From this calculation, we can see that Patrick will have more money after 2 years, $372.68 as compared to Brooklyn's $326.64

It is important to note that interest rate and the frequency of compounding has a big role in this case, which results in a difference of amount.

Answer 2

Patrick

A(2) = 300(1 + 0.03 / 4)⁽⁴⁾⁽²⁾

Brooklyn

A(2) = 300(1 + 0.05 / 12)^(12)(2)

This is basic computation. Nothing to do with Algebra.