If $22,000 is deposited in a bank account at 2.75% interest, how much will be in the account after 9 years?

If $22,000 is deposited in a bank account at 2.75% interest, how much will be in the account after 9 years?

• A. $24,567.30
• B. $26,073.45
• C. $27,135.94
• D. $28,084.01

Answer: (D)

To determine the amount in the bank account after 9 years with a principal of $22,000 at an interest rate of 2.75%, it's important to clarify that the total amount in the account can be calculated using the formula for compound interest. The compound interest formula is: \[ A = P(1 + r)^n \] where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial deposit or investment). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of years the money is invested or borrowed. Plugging in the values: - \( P = 22,000 \) - \( r = 0.0275 \) (which is 2.75% written as a decimal) - \( n = 9 \) Now, calculate the accumulated amount: \[ A = 22,000 \times (1 + 0.0275)^9 \] Calculating inside the parentheses first: \[ A = 22,000 \times (1.0275)^9 \] Next, compute \( (1.0275)^9 \). This

To determine the amount in the bank account after 9 years with a principal of $22,000 at an interest rate of 2.75%, it's important to clarify that the total amount in the account can be calculated using the formula for compound interest. The compound interest formula is:

[ 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 deposit or investment).

• ( r ) is the annual interest rate (decimal).

• ( n ) is the number of years the money is invested or borrowed.

Plugging in the values:

• ( P = 22,000 )

• ( r = 0.0275 ) (which is 2.75% written as a decimal)

• ( n = 9 )

Now, calculate the accumulated amount:

[ A = 22,000 \times (1 + 0.0275)^9 ]

Calculating inside the parentheses first:

[ A = 22,000 \times (1.0275)^9 ]

Next, compute ( (1.0275)^9 ). This