Question

70
8/15
Find the balance in the account after the given period.
$3400 principal earning 3.6% compounded annually after 2 years
3.47 AM 2024-0...00.00 AM
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2024-0...48.00 AM
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2024-0...48.40 AM
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2024-0...40.01 AM
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2024-0...40.30 AM
$3,675.39
$3,649.21
$6,288.64
$3,420.43

Answer 1

To calculate the balance in an account after a certain period of time with a principal amount (P), an interest rate (r), and compounding annually (t), you 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 amount of money).
- \( r \) is the annual interest rate (decimal).
- \( t \) is the number of years the money is invested or borrowed.

Given:
- Principal \( P = 3400 \)
- Annual interest rate \( r = 3.6\% = 0.036 \)
- Time \( t = 2 \) years

Plugging in the values:

\[ A = 3400(1 + 0.036)^2 \]
\[ A = 3400(1.036)^2 \]
\[ A = 3400(1.073296) \]
\[ A \approx 3649.20 \]

Thus, after 2 years, the balance in the account will be approximately **$3,649.20**.

Among the given options, the closest amount is **$3,649.21**.