how much would you need to deposit in an account now in order to have $10,000 in the account in 11 years…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula for present value is $PV=\frac{FV}{(1 + \frac{r}{n})^{nt}}$, where $PV$ is the present value (the amount to be deposited now), $FV$ is the future value, $r$ 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 the given values to the appropriate form

We have $FV = 10100$, $r=0.046$ (since $4.6%=0.046$), $n = 12$ (compounded monthly), and $t = 11$.

Step3: Substitute the values into the formula

$PV=\frac{10100}{(1+\frac{0.046}{12})^{12\times11}}$. First, calculate the value inside the parentheses: $\frac{0.046}{12}\approx0.003833$, then $1+\frac{0.046}{12}=1 + 0.003833=1.003833$. Next, calculate the exponent: $12\times11 = 132$. So, $(1.003833)^{132}\approx1.64777$. Then, $PV=\frac{10100}{1.64777}\approx6129.49$.

Answer:

$6129.49$