juanipa manglimont inherited $27,500 from her father. she placed the money in an investment earning 6%…

juanipa manglimont inherited $27,500 from her father. she placed the money in an investment earning 6% compounded quarterly. find the future value at the end of 8 years. the future value at the end of 8 years is $ (round to the nearest cent as needed.)

juanipa manglimont inherited $27,500 from her father. she placed the money in an investment earning 6% compounded quarterly. find the future value at the end of 8 years. the future value at the end of 8 years is $ (round to the nearest cent as needed.)

Answer

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the future value, $P$ 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=$27500$, $r = 6%=0.06$, $n = 4$ (compounded quarterly), and $t = 8$ years.

Step3: Substitute values into the formula

$A=27500(1 +\frac{0.06}{4})^{4\times8}=27500(1 + 0.015)^{32}$.

Step4: Calculate the value inside the parentheses

$1+0.015 = 1.015$.

Step5: Calculate the exponent

$(1.015)^{32}\approx1.610323$.

Step6: Calculate the future value

$A = 27500\times1.610323\approx44283.88$.

Answer:

$44283.88$