10
Multiple Choice
1 point
hboard

An investor deposited in an investment account.

The account pays interest compounded annually.

The investor leaves the money in the account for 2 years.

The investor make no additional deposits or withdrawals.

What is the balance in the account at the end of 2 years?
$6,686.21

$6,484.06
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Ask by Byrd Chandler. in the United States

Jan 26,2025

Question

10
Multiple Choice
1 point
hboard

An investor deposited in an investment account.

The account pays interest compounded annually.

The investor leaves the money in the account for 2 years.

The investor make no additional deposits or withdrawals.

What is the balance in the account at the end of 2 years?
$6,686.21

$6,484.06
History
5

88
6
Mastery
7

Clear my selection
Help
Previous

Ask by Byrd Chandler. in the United States

Jan 26,2025

UpStudy AI · Accepted Answer

To find the balance in the investment account at the end of 2 years with an initial deposit of $$ P = 6100 $$ and an annual interest rate of $$ r = 3.1\% $$ compounded annually, we can use the formula for compound interest:

$$
A = P(1 + r)^t
$$

where:
- $$ A $$ is the amount of money accumulated after n years, including interest.
- $$ P $$ is the principal amount (the initial deposit).
- $$ r $$ is the annual interest rate (decimal).
- $$ t $$ is the number of years the money is invested or borrowed.

### Step 1: Convert the interest rate from percentage to decimal
$$
r = \frac{3.1}{100} = 0.031
$$

### Step 2: Substitute the known values into the formula
$$
A = 6100(1 + 0.031)^2
$$

### Step 3: Calculate $$ (1 + r) $$
$$
1 + r = 1 + 0.031 = 1.031
$$

### Step 4: Calculate $$ (1.031)^2 $$
$$
(1.031)^2 = 1.062061
$$

### Step 5: Calculate the final amount $$ A $$
$$
A = 6100 \times 1.062061
$$

Now, let's perform the calculation for $$ A $$.
Calculate the value by following steps:
- step0: Calculate:
  $$6100\times 1.062061$$
- step1: Multiply the numbers:
  $$6478.5721$$
The calculation gives us:

$$
A \approx 6478.5721
$$

### Final Step: Round to two decimal places
The balance in the account at the end of 2 years is approximately $$ \$ 6,478.57 $$.

### Conclusion
Among the provided options, the closest match is:

$$\$ 6,478.20$$

Thus, the correct answer is $$ \$ 6,478.20 $$.
The balance in the account at the end of 2 years is approximately \$6,478.20.

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