suppose that $2000 is invested at a rate of 2...
suppose that $2000 is invested at a rate of 2.1%, compounded monthly. assuming that no withdrawals are made, find the total amount after 7 years. do not round any intermediate computations, and round your answer to the nearest cent.
Answer
# Explanation:
## Step1: Identify compound - interest formula
The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times compounded per year, and $t$ is the number of years.
## Step2: Convert values to appropriate form
Given $P=\$2000$, $r = 2.1\%=0.021$, $n = 12$ (compounded monthly), and $t = 7$ years.
## Step3: Substitute values into formula
$A=2000(1 +\frac{0.021}{12})^{12\times7}$.
First, calculate $\frac{0.021}{12}=0.00175$.
Then, $1+\frac{0.021}{12}=1 + 0.00175=1.00175$.
Next, $12\times7 = 84$.
So, $A = 2000\times(1.00175)^{84}$.
## Step4: Calculate the result
$(1.00175)^{84}\approx1.156777$.
$A=2000\times1.156777=\$2313.554$.
Rounding to the nearest cent, $A\approx\$2313.55$.
# Answer:
$\$2313.55$