a saving account that earns 3.2% interest compounded bi - annually has a balance of $6,049.15 after 6 years…

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Here, $r = 0.032$, $n = 2$ (bi - annually), $t = 6$ years, and $A=$6049.15$.

Step2: Substitute values into the formula and solve for $P$

$6049.15=P(1 +\frac{0.032}{2})^{2\times6}$ $6049.15=P(1 + 0.016)^{12}$ $6049.15=P(1.016)^{12}$ First, calculate $(1.016)^{12}\approx1.21$. Then, $P=\frac{6049.15}{(1.016)^{12}}\approx\frac{6049.15}{1.21}\approx5000$.

Step3: Calculate the interest earned

The interest earned $I=A - P$. Substitute $A = 6049.15$ and $P = 5000$ into the formula. $I=6049.15−5000 = 1049.15$

Answer:

A. $1,049.15$