Question

Find the balance after 10 years of a $30,000 savings account that pays 10% interest compounded yearly.(1 point)
Responses

$2,245,256.05
$2,245,256.05

$33,154.81
$33,154.81

$77,812.27
$77,812.27

$112,070.90
$112,070.90

Answer 1

To calculate the balance of a savings account after 10 years with compound interest, you can use the formula:

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

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 years the money is invested or borrowed.

Given:
- \( P = 30,000 \)
- \( r = 10\% = 0.10 \)
- \( n = 10 \)

Plugging in the values:

\[ A = 30,000(1 + 0.10)^{10} \]
\[ A = 30,000(1.10)^{10} \]
\[ A = 30,000(2.59374) \] (approximately)
\[ A = 77,812.20 \]

Thus, the balance after 10 years will be approximately **$77,812.27**.

Therefore, the correct response is:

**$77,812.27**