vincent puts $2,000.00 into an account to use for school expenses. the account earns 10% interest…

vincent puts $2,000.00 into an account to use for school expenses. the account earns 10% interest, compounded quarterly. how much will be in the account after 6 years? use the formula $a = p(1+\frac{r}{n})^{nt}$, 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.

vincent puts $2,000.00 into an account to use for school expenses. the account earns 10% interest, compounded quarterly. how much will be in the account after 6 years? use the formula $a = p(1+\frac{r}{n})^{nt}$, 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

$P = 2000$, $r=0.10$ (since 10% = 0.10), $n = 4$ (compounded quarterly), $t = 6$.

Step2: Substitute values into formula

$A=2000\left(1+\frac{0.10}{4}\right)^{4\times6}$ $A = 2000\left(1 + 0.025\right)^{24}$

Step3: Calculate the value inside parentheses

$1+0.025=1.025$

Step4: Calculate the exponentiation

$1.025^{24}\approx1.8087269$

Step5: Multiply by principal

$A=2000\times1.8087269 = 3617.4538$

Step6: Round to nearest cent

$A\approx3617.45$

Answer:

$3617.45$