nolan deposited $2300 into a savings account for which interest is compounded weekly at a rate of 2.12%. how…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Here, $P=$2300$, $r = 0.0212$ (since $2.12%=0.0212$), $n = 52$ (compounded weekly), and $t = 7$.

Step2: Calculate the amount $A$

$A=2300(1 +\frac{0.0212}{52})^{52\times7}$ First, calculate the value inside the parentheses: $\frac{0.0212}{52}\approx0.0004077$. Then $1+\frac{0.0212}{52}=1 + 0.0004077=1.0004077$. Next, calculate the exponent: $52\times7 = 364$. So, $A = 2300\times(1.0004077)^{364}$. $(1.0004077)^{364}\approx1.15994$. Then $A=2300\times1.15994=$2667.862$.

Step3: Calculate the interest $I$

The interest $I=A - P$. $I=2667.862-2300=$367.862\approx$367.87$.

Answer:

$367.87$ (corresponding to the third option)