olivia puts $4,000.00 into an account to use for school expenses. the account earns 10% interest, compounded…

olivia puts $4,000.00 into an account to use for school expenses. the account earns 10% interest, compounded monthly. how much will be in the account after 8 years? use the formula $a = p\\left(1 + \\frac{r}{n}\\right)^{nt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, $n$ is the number of times per year that the interest is compounded, and $t$ is the time in years. round your answer to the nearest cent.

olivia puts $4,000.00 into an account to use for school expenses. the account earns 10% interest, compounded monthly. how much will be in the account after 8 years? use the formula $a = p\\left(1 + \\frac{r}{n}\\right)^{nt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, $n$ is the number of times per year that the interest is compounded, and $t$ is the time in years. round your answer to the nearest cent.

Answer

Explanation:

Step1: Identify the values

We have ( P = 4000 ), ( r = 0.10 ) (10% as a decimal), ( n = 12 ) (compounded monthly), and ( t = 8 ).

Step2: Substitute into the formula

[ \begin{align*} A&=4000\left(1+\frac{0.10}{12}\right)^{12\times8}\ &=4000\left(1+\frac{0.10}{12}\right)^{96} \end{align*} ] First, calculate the value inside the parentheses: ( 1+\frac{0.10}{12}\approx1 + 0.008333=1.008333 )

Step3: Calculate the exponent

Now, raise ( 1.008333 ) to the power of 96. Using a calculator, ( 1.008333^{96}\approx2.219640 )

Step4: Multiply by the principal

Multiply this result by 4000: ( A = 4000\times2.219640 = 8878.56 )

Answer:

$8878.56