kenji and shawna deposit $6,000.00 into a savings account which earns 15% interest compounded quarterly…

kenji and shawna deposit $6,000.00 into a savings account which earns 15% interest compounded quarterly. they want to use the money in the account to go on a trip in 2 years. how much will they be able to spend? 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.

kenji and shawna deposit $6,000.00 into a savings account which earns 15% interest compounded quarterly. they want to use the money in the account to go on a trip in 2 years. how much will they be able to spend? 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

$P = 6000$, $r=0.15$, $n = 4$ (quarter - ly compounding), $t = 2$

Step2: Substitute into the formula

$A=P(1 +\frac{r}{n})^{nt}=6000(1+\frac{0.15}{4})^{4\times2}$ First, calculate the value inside the parentheses: $\frac{0.15}{4}=0.0375$, then $1 + 0.0375=1.0375$. And $nt=4\times2 = 8$. So $A = 6000\times(1.0375)^{8}$.

Step3: Calculate $(1.0375)^{8}$

$(1.0375)^{8}\approx1.346855$.

Step4: Calculate $A$

$A=6000\times1.346855 = 8081.13$.

Answer:

$8081.13$