the value of yongs investment account increases at a rate that is proportional at any time to the value of…

Explanation:

Step1: Identify the compound - growth formula

The formula for compound - growth when the growth is proportional to the current amount is $A = P(1 + r)^{\frac{t}{n}}$, where $P$ is the principal amount, $r$ is the growth rate, $t$ is the time elapsed, and $n$ is the time - interval for the growth rate. Here, $P=$2000$, $r = 0.1$, $n = 4$ years, and $t = 7$ years.

Step2: Substitute the values into the formula

$A=2000\times(1 + 0.1)^{\frac{7}{4}}$. First, calculate the exponent: $\frac{7}{4}=1.75$. Then, calculate $(1 + 0.1)^{1.75}=1.1^{1.75}$. Using a calculator, $1.1^{1.75}\approx1.18159$.

Step3: Find the final amount

Multiply the initial amount by the result of the exponentiation: $A = 2000\times1.18159=$2363.18\approx$2363$.

Answer:

C. $$2363$