Answer:
Brooklyn's
Step-by-step explanation:
Recall the formula for annual compound interest: [tex]A=P(1+\frac{r}{n})^n^t[/tex].
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!
