jake opened a savings account and deposited $6,290.00 as principal. the account earns 9% interest…

jake opened a savings account and deposited $6,290.00 as principal. the account earns 9% interest, compounded quarterly. what is the balance after 5 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.

jake opened a savings account and deposited $6,290.00 as principal. the account earns 9% interest, compounded quarterly. what is the balance after 5 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

$P = 6290$, $r=0.09$, $n = 4$, $t = 5$

Step2: Substitute values into formula

$A=6290\left(1+\frac{0.09}{4}\right)^{4\times5}$

Step3: Calculate the value inside the parentheses

$1+\frac{0.09}{4}=1 + 0.0225=1.0225$

Step4: Calculate the exponent

$4\times5 = 20$

Step5: Calculate the power

$(1.0225)^{20}\approx1.5605$

Step6: Calculate the final amount

$A = 6290\times1.5605\approx9815.55$

Answer:

$9815.55$