how much money should be deposited today in an account that earns 4.5% compounded monthly so that it will…

Explanation:

Step1: Identify the compound - interest formula

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

Step2: Convert the given values to the appropriate form

We have $A = 13000$, $r=0.045$ (since $4.5%=0.045$), $n = 12$ (compounded monthly), and $t = 3$.

Step3: Substitute the values into the formula

$P=\frac{13000}{(1+\frac{0.045}{12})^{12\times3}}$. First, calculate the value inside the parentheses: $\frac{0.045}{12}=0.00375$, and $1+\frac{0.045}{12}=1.00375$. Then, calculate the exponent: $12\times3 = 36$. So, $(1.00375)^{36}\approx1.143204$. Finally, $P=\frac{13000}{1.143204}\approx11371.53$.

Answer:

$11371.53$