principal: $5000 interest rate: 3.75% time: 25 years compounded monthly state the future account balance…

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.

Step2: Convert values to appropriate form

Given $P = 5000$, $r=0.0375$ (since $3.75%=0.0375$), $n = 12$ (compounded monthly), and $t = 25$.

Step3: Substitute values into the formula

$A=5000(1 +\frac{0.0375}{12})^{12\times25}$. First, calculate the value inside the parentheses: $\frac{0.0375}{12}=0.003125$, then $1+\frac{0.0375}{12}=1.003125$. Next, calculate the exponent: $12\times25 = 300$. So, $A = 5000\times(1.003125)^{300}$.

Step4: Calculate the final amount

$(1.003125)^{300}\approx2.54986$, and $A=5000\times2.54986 = 12749.3$.

Answer:

$12,749.30$