how much should be invested now at 4.3% compounded monthly to have $36,000 in 16 years?

Explanation:

Step1: Identify 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), $n$ is the number of times compounded per year, and $t$ is the number of years.

Step2: Convert values to appropriate form

Given $A = 36000$, $r=0.043$ (since $4.3%=0.043$), $n = 12$ (compounded monthly), and $t = 16$.

Step3: Substitute values into formula

$P=\frac{36000}{(1+\frac{0.043}{12})^{12\times16}}$ First, calculate the value inside the parentheses: $\frac{0.043}{12}\approx0.0035833$, then $1+\frac{0.043}{12}=1 + 0.0035833=1.0035833$. Next, calculate the exponent: $12\times16 = 192$. So, $(1.0035833)^{192}\approx1.9877$. Then, $P=\frac{36000}{1.9877}\approx18101.22$.

Answer:

$18101.22$