Question

you plan to deposit $2,250 into a savings account that has a 6.33% interest rate compounded monthly. what will be the balance of your savings account after 1 years?
use this formula:
$a = p(1 + \frac{r}{n})^{nt}$
enter the dollar amount rounded to the nearest cent.
your answer:

Explanation:

Step1: Identify the values

We know that \( P = 2250 \) (principal amount), \( r = 6.33\% = 0.0633 \) (annual interest rate), \( n = 12 \) (number of times interest is compounded per year, since it's monthly), and \( t = 1 \) (number of years).

Step2: Substitute into the formula

Substitute the values into the compound - interest formula \( A = P(1+\frac{r}{n})^{nt} \).
First, calculate \( \frac{r}{n}=\frac{0.0633}{12}= 0.005275 \).
Then, calculate \( 1+\frac{r}{n}=1 + 0.005275=1.005275 \).
Next, calculate \( nt=12\times1 = 12 \).
Now, calculate \( (1 + \frac{r}{n})^{nt}=(1.005275)^{12}\approx1.0653 \) (using a calculator to find the power).
Finally, calculate \( A=P(1 + \frac{r}{n})^{nt}=2250\times1.0653\approx2250\times1.0653 = 2407.025\approx2407.03 \)

Answer:

\( \$2407.03 \)