Question

jaina and tomas compare their compound interest accounts to see how much they will have in the accounts after three years. they substitute their values shown below into the compound interest formula.
compound interest accounts

name	principal	interest rate	number of years	compounded
tomas	$400	4%	3	once a year

$a = p(1 + r)^t$
which pair of equations would correctly calculate their compound interests?
\\(\bigcirc\\) jaina: \\(a = 400(1 + 0.07)^3\\), tomas: \\(a = 300(1 + 0.04)^3\\)
\\(\bigcirc\\) jaina: \\(a = 300(1 + 0.03)^7\\), tomas: \\(a = 400(1 + 0.03)^4\\)
\\(\bigcirc\\) jaina: \\(a = 400(1 + 0.03)^7\\), tomas: \\(a = 300(1 + 0.03)^4\\)
\\(\bigcirc\\) jaina: \\(a = 300(1 + 0.07)^3\\), tomas: \\(a = 400(1 + 0.04)^3\\)

Explanation:

Step1: Match Jaina's values to formula

Jaina's principal $P=300$, rate $r=0.07$, time $t=3$. Substitute into $A=P(1+r)^t$:
$A = 300(1+0.07)^3$

Step2: Match Tomas's values to formula

Tomas's principal $P=400$, rate $r=0.04$, time $t=3$. Substitute into $A=P(1+r)^t$:
$A = 400(1+0.04)^3$

Step3: Identify correct option

Compare the derived equations to the given choices.

Answer:

Jaina: $A = 300(1+0.07)^3$, Tomas: $A = 400(1+0.04)^3$