Patrick and Brooklyn are making decisions about their bank accounts. Patrick wants to deposit $200 as a principal amount, with an interest of 2% compounded quarterly. Brooklyn wants to deposit $200 as the principal amount, with an interest of 4% compounded monthly. Explain which method results in more money after 2 years. Show all work.

Where A is the total amount, P is the initial or principal amount, r is the rate in decimal form, n is the number of times per year the interest is compounded and t is the number of years that the interest is compounded.

So let's apply this formula for each person, starting with Patrick.

P = 200

r = 0.02

n = 4 (quarterly means 4 times a year)

t = 2 (the question asks to compare Patrick and Brooklyn's bank accounts after 2 years)

[tex]A=200(1+\frac{0.02}{4})^4^(^2^)=200(\frac{4.02}{4} )^8=208.14[/tex]

Let's move on to Brooklyn.

P = 200

r = 0.04

n = 12 (monthly means 12 months in a year)

t = 2

[tex]A=200(1+\frac{0.04}{4})^1^2^(^2^)=200(\frac{4.04}{4} )^2^4=253.95[/tex]

Since 253.95 is greater than 208.14, Brooklyn's method resulted in more money.

Let me know if you have any more questions!