Answer:
I(x) = $8,000(1.08^x) - $8,000
I(10) = $8,000(1.08^10) - $8,000
= $9,271.40
Final amount accumulated = $17271.40
Interest accrued = $9271.40
We can derive a formula for the amount accumulated at the end of period of time, and from there, calculate the interest.
[tex]\large \textsf{Let A$_{\sf n}$ = amount in account after $n$ terms}\\\textsf{P = principal (amount put in initially)}\\\textsf{r = interest rate}\\\textsf{R = $\sf \left(1+\frac{r}{100}\right)$ = compounding factor}[/tex]
Compound interest differs from simple interest. Simple interest is where interest is earned from the principal. Simple interest follows the formula I=PrN/100, where I = simple interest.
Compound interest is where additional interest is earned on the principal plus prior interest already earned.
To derive the formula, we can consider what happens each term, and find a pattern that evolves:
[tex]\sf A_1 = PR\\A_2 = A_1R\\\phantom{A_2}= PR^2 \\A_3 = A_2R\\\phantom{A_3}= PR^3[/tex]
[tex]\boxed{\large \textsf{$\therefore \sf A_n = PR^n$ is the formula for compound interest}}[/tex]
And so n = 10; P = 8000; r = 8; R = 1.08
[tex]\large \textsf{$\therefore \sf A_{10} = 8000\left(1.08\right)^{10}$}\\\textsf{$\phantom{\therefore \sf A_{10}}= 17271.40$}\\\\\textsf{$\therefore$ Amount in account after 10 years is $\$17271.40}\\\\[/tex]
To calculate interest, subtract principal from final amount:
[tex]\large \textsf{$\sf Interest = final\ amount - principal$}\\\\\text{$\phantom{\sf Interest} = 17271.40 - 8000$}\\\\\text{$\therefore \sf Interest = \$9271.40$}[/tex]
To learn more about compound interest:
https://brainly.com/question/22621039
