Final answer:
The final balance of a $4,000 initial investment at a 6.2% annual interest rate compounded annually after 10 years would be closest to $7,276. The provided options lead to the selection of option C. Approximately $7,264.00 as the closest to the calculated amount.
Step-by-step explanation:
The student is asking about the final balance of an initial investment with compound interest in a retirement account after 10 years. When an employee contributes $4,000 to this account with an annual interest rate of 6.2%, compounded annually, no further deposits or withdrawals are made. We can use the compound interest formula:
A = P(1 + r/n)^(nt)
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 times that interest is compounded per year.
- t is the time the money is invested for, in years.
Since the interest is compounded annually, n is 1. Plugging the values into the formula gives us:
A = $4,000(1 + 0.062/1)^(1*10) = $4,000(1.062)^10
Calculating the power of 1.062 raised to the 10th power and then multiplying by $4,000, we get the balance at the end of 10 years. The correct answer will be the one that is closest to this calculated amount.
Using a calculator, we compute:
A = $4,000 * (1.062)^10 ≈ $4,000 * 1.819 = $7,276
The closest answer to $7,276 is C. Approximately $7,264.00