Question

The formula where is the amount invested, is the rate and is the time in years, can be used to find , the total amount at any given time.

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If $1,400 is invested at a rate of 4.25% per year, then there will be approximately Response area in the account after 14 years.

$2,500$2,700$25,000$254,000
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Answer 1

To find the total amount \( A \) in the account after 14 years, we can use the formula for compound interest, which is given by:

\[
A = P(1 + r)^t
\]

Where:
- \( A \) is the total amount after time \( t \),
- \( P \) is the principal amount (initial investment),
- \( r \) is the annual interest rate (as a decimal),
- \( t \) is the time in years.

Given:
- \( P = 1400 \)
- \( r = 4.25\% = 0.0425 \)
- \( t = 14 \)

We can plug these values into the formula:

\[
A = 1400(1 + 0.0425)^{14}
\]

Calculating the inside of the parentheses first:

\[
1 + 0.0425 = 1.0425
\]

Now raising it to the power of 14:

\[
(1.0425)^{14}
\]

Using a calculator:

\[
(1.0425)^{14} \approx 1.749
\]

Now we multiply by the principal amount:

\[
A = 1400 \times 1.749 \approx 2448.6
\]

Thus, the approximate total amount in the account after 14 years will be around $2,448.60.

Now, looking at the provided response options:

- $2,500
- $2,700
- $25,000
- $254,000

The closest round figure is **$2,500**.

So the answer is **$2,500**.