Final answer:
The final amount after one year in an account with $4000 at a 6.2% annual interest rate compounded semiannually will be approximately $4251.84, so the correct answer is d) $4251.
Step-by-step explanation:
To determine the final amount in a savings account with an initial principal of $4000, an annual interest rate of 6.2% compounded semiannually after one year, we can use the formula for compound interest:
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 or borrowed for, in years.
Plugging the values into the formula:
A = 4000(1 + 0.062/2)2×1 = 4000(1 + 0.031)2 = 4000(1.031)2
A = 4000 × 1.062961 = $4251.84
The final amount after one year will be approximately $4251.84. Therefore, the correct answer is d) $4251.