approximately how much principal would need to be placed into an account earning 3.575% interest compounded…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the accumulated value, $P$ is the principal, $r$ 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. We need to solve for $P$, so $P=\frac{A}{(1 +\frac{r}{n})^{nt}}$.

Step2: Convert values to appropriate form

The annual interest rate $r = 3.575%=0.03575$, the number of times compounded per year $n = 4$ (quarterly compounding), the number of years $t = 30$, and the accumulated value $A=68000$.

Step3: Calculate the exponent

$nt=4\times30 = 120$ and $\frac{r}{n}=\frac{0.03575}{4}=0.0089375$.

Step4: Calculate the denominator

$(1+\frac{r}{n})^{nt}=(1 + 0.0089375)^{120}$. Using a calculator, $(1 + 0.0089375)^{120}\approx2.878$.

Step5: Calculate the principal

$P=\frac{A}{(1+\frac{r}{n})^{nt}}=\frac{68000}{2.878}\approx23628\approx23706$.

Answer:

A. $23,706$