how much money should be deposited today in an account that earns 3.5% compounded monthly so that it will…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula for present value is $P = \frac{A}{(1+\frac{r}{n})^{nt}}$, where $A$ is the future value, $r$ is the annual interest rate (in decimal), $n$ is the number of times compounded per year, and $t$ is the number of years.

Step2: Convert values to appropriate form

Given $A = 14000$, $r=0.035$ (since $3.5%=0.035$), $n = 12$ (compounded monthly), and $t = 3$.

Step3: Substitute values into the formula

$P=\frac{14000}{(1 +\frac{0.035}{12})^{12\times3}}$. First, calculate the value inside the parentheses: $\frac{0.035}{12}\approx0.0029167$, then $1+\frac{0.035}{12}=1 + 0.0029167=1.0029167$. Next, calculate the exponent: $12\times3 = 36$. So, $(1+\frac{0.035}{12})^{12\times3}=(1.0029167)^{36}$. Using a calculator, $(1.0029167)^{36}\approx1.110903$. Then $P=\frac{14000}{1.110903}\approx12602.34$.

Answer:

$12602.34$