perry and nora deposit $5,000.00 into a savings account which earns 5% interest compounded monthly. they…

perry and nora deposit $5,000.00 into a savings account which earns 5% interest compounded monthly. 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.

perry and nora deposit $5,000.00 into a savings account which earns 5% interest compounded monthly. 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 values

$P = 5000$, $r=0.05$, $n = 12$, $t = 2$

Step2: Substitute into formula

$A=5000\left(1+\frac{0.05}{12}\right)^{12\times2}$

Step3: Calculate inside parentheses

$1+\frac{0.05}{12}=1+\frac{1}{240}=\frac{240 + 1}{240}=\frac{241}{240}$

Step4: Calculate exponent

$12\times2 = 24$

Step5: Calculate power

$A = 5000\times\left(\frac{241}{240}\right)^{24}$ $\left(\frac{241}{240}\right)^{24}\approx1.1049413$

Step6: Find final amount

$A=5000\times1.1049413 = 5524.7065\approx5524.71$

Answer:

$5524.71$