after 8 years, what is the total amount of a compound interest investment of $25,000 at 3% interest…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ 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 values to appropriate form

Given $P=$25000$, $r = 0.03$ (since $3%=0.03$), $n = 4$ (compounded quarterly), and $t = 8$ years.

Step3: Substitute values into formula

$A=25000(1 +\frac{0.03}{4})^{4\times8}=25000(1 + 0.0075)^{32}$.

Step4: Calculate the value inside the parentheses

$1+0.0075=1.0075$.

Step5: Calculate the exponent

$(1.0075)^{32}\approx1.270111$.

Step6: Calculate the final amount

$A = 25000\times1.270111=$31752.78$.

Answer:

D. $$31,752.78$