find the missing final amount (future value) and interest earned.\n\ncomplete the table.\n(round to the…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is (A = P\left(1+\frac{r}{n}\right)^{nt}), where (P) is the principal, (r) is the annual interest rate (in decimal form), (n) is the number of times compounded per year, and (t) is the number of years.

Given (P=$825), (r = 0.05) (since (5%=0.05)), (n = 4) (compounded quarterly), and (t = 8) years.

Step2: Calculate the final amount (A)

Substitute the values into the formula: [ \begin{align*} A&=825\left(1+\frac{0.05}{4}\right)^{4\times8}\ &=825\left(1 + 0.0125\right)^{32}\ &=825\times(1.0125)^{32} \end{align*} ] Using a calculator, ((1.0125)^{32}\approx1.4888637) [ A=825\times1.4888637\approx$1228.31 ]

Step3: Calculate the compound interest (I)

The compound interest formula is (I=A - P) [ I=1228.31-825=$403.31 ]

Answer:

The final amount is ($1228.31) and the compound interest is ($403.31)