diego and natalie deposit $3,000.00 into a savings account which earns 3% interest compounded monthly. they…

diego and natalie deposit $3,000.00 into a savings account which earns 3% 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. $

diego and natalie deposit $3,000.00 into a savings account which earns 3% 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 the values of variables

$P = 3000$, $r=0.03$ (since 3% = 0.03), $n = 12$ (compounded monthly), $t = 2$.

Step2: Substitute values into the formula

$A=3000\left(1+\frac{0.03}{12}\right)^{12\times2}$ First, calculate the value inside the parentheses: $\frac{0.03}{12}=0.0025$, then $1 + 0.0025=1.0025$. And $12\times2 = 24$. So $A = 3000\times(1.0025)^{24}$.

Step3: Calculate $(1.0025)^{24}$

Using a calculator, $(1.0025)^{24}\approx1.061757$.

Step4: Calculate the final amount $A$

$A=3000\times1.061757 = 3185.271$. Rounding to the nearest cent, $A\approx3185.27$.

Answer:

$3185.27$