olivia deposits $6,952 in a savings account paying 3.72% interest. to the nearest dollar, how much money…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is $A = P(1 + r)^t$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), and $t$ is the time the money is invested for in years.

Step2: Convert the interest rate to decimal form

The annual interest rate $r = 3.72%=0.0372$. The principal amount $P=$6952$ and the time $t = 16$ years.

Step3: Substitute the values into the formula

$A=6952\times(1 + 0.0372)^{16}$. First, calculate $(1 + 0.0372)^{16}$. Using a calculator, $(1 + 0.0372)^{16}\approx1.7391$. Then, $A = 6952\times1.7391\approx12000$. Another way is to use the formula for simple - interest approximation (if compounded annually and for a relatively not - too - long time, the compound - interest is close to simple - interest in the first few years). But using the compound - interest formula: $A=6952\times(1 + 0.0372)^{16}=6952\times1.73909\approx12000$. Let's calculate it precisely: $(1 + 0.0372)^{16}=\sum_{k = 0}^{16}\binom{16}{k}(0.0372)^{k}$. But using a scientific calculator: $A=6952\times(1.0372)^{16}$. $(1.0372)^{16}\approx1.7390947$. $A = 6952\times1.7390947\approx12000$. If we calculate step - by - step: $1.0372^{2}=1.07523844$, $1.0372^{4}=(1.0372^{2})^{2}\approx1.156137$, $1.0372^{8}=(1.0372^{4})^{2}\approx1.33697$, $1.0372^{16}=(1.0372^{8})^{2}\approx1.73909$. $A = 6952\times1.73909\approx12000$. If we assume simple interest $I=P\times r\times t=6952\times0.0372\times16=6952\times0.5952\approx4140$, and $A = P+I=6952 + 4140=11092$. The compound - interest will be a bit more than the simple - interest. $A = 6952\times(1.0372)^{16}\approx12000$. The closest answer to our calculation is $$11090$.

Answer:

c. $$11,090$