To determine how much Nicole will have in her account after 9 years with an annual interest rate of 2.4% compounded annually, we can use the compound interest formula:

$$ A = P \left(1 + \frac{r}{n}\right)^{nt} $$

where:
- $ A $ is the amount of money accumulated after n years, including interest.
- $ P $ is the principal amount (the initial amount of money).
- $ r $ is the annual interest rate (decimal).
- $ n $ is the number of times that interest is compounded per year.
- $ t $ is the time the money is invested for in years.

Given:
- $ P = 4000 $
- $ r = 2.4\% = 0.024 $
- $ n = 1 $ (since the interest is compounded annually)
- $ t = 9 $

Plugging these values into the formula, we get:

$$ A = 4000 \left(1 + \frac{0.024}{1}\right)^{1 \times 9} $$

Simplify the expression inside the parentheses:

$$ A = 4000 \left(1 + 0.024\right)^{9} $$
$$ A = 4000 \left(1.024\right)^{9} $$

Now, calculate $ (1.024)^{9} $:

$$ (1.024)^{9} \approx 1.233122 $$

Next, multiply this result by the principal amount:

$$ A = 4000 \times 1.233122 $$
$$ A \approx 4932.49 $$

Therefore, after 9 years, Nicole will have approximately $4932.49 in her account.

Question

To determine how much Nicole will have in her account after 9 years with an annual interest rate of 2.4% compounded annually, we can use the compound interest formula:

$$ A = P \left(1 + \frac{r}{n}\right)^{nt} $$

where:
- $ A $ is the amount of money accumulated after n years, including interest.
- $ P $ is the principal amount (the initial amount of money).
- $ r $ is the annual interest rate (decimal).
- $ n $ is the number of times that interest is compounded per year.
- $ t $ is the time the money is invested for in years.

Given:
- $ P = 4000 $
- $ r = 2.4\% = 0.024 $
- $ n = 1 $ (since the interest is compounded annually)
- $ t = 9 $

Plugging these values into the formula, we get:

$$ A = 4000 \left(1 + \frac{0.024}{1}\right)^{1 \times 9} $$

Simplify the expression inside the parentheses:

$$ A = 4000 \left(1 + 0.024\right)^{9} $$
$$ A = 4000 \left(1.024\right)^{9} $$

Now, calculate $ (1.024)^{9} $:

$$ (1.024)^{9} \approx 1.233122 $$

Next, multiply this result by the principal amount:

$$ A = 4000 \times 1.233122 $$
$$ A \approx 4932.49 $$

Therefore, after 9 years, Nicole will have approximately $4932.49 in her account.

Knowee AI · Accepted Answer