darnel and mabel deposit $7,892.00 into a savings account which earns 11% interest compounded quarterly…

darnel and mabel deposit $7,892.00 into a savings account which earns 11% 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.

darnel and mabel deposit $7,892.00 into a savings account which earns 11% 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

$P = 7892$, $r=0.11$, $n = 4$ (quarter - ly compounding), $t = 2$

Step2: Substitute into the formula

$A=7892\left(1+\frac{0.11}{4}\right)^{4\times2}$

Step3: Calculate the value inside the parentheses

$1+\frac{0.11}{4}=1 + 0.0275=1.0275$

Step4: Calculate the exponent

$4\times2 = 8$

Step5: Calculate the power

$(1.0275)^{8}\approx1.233677$

Step6: Multiply by the principal

$A = 7892\times1.233677\approx9736.68$

Answer:

$9736.68$