Final answer:
To calculate the final balance with compound interest, one applies the formula A = P(1 + r/n)^(nt). After substituting the values ($4000 principal, 3% interest, compounded annually, over 6 years), the balance is found to be $4776.21, meaning none of the provided choices are correct.
Step-by-step explanation:
To find the balance in the account after 6 years when $4000 is deposited with an annual compound interest rate of 3%, we 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 (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
In this problem:
- P is $4000
- r is 0.03 (3% expressed as a decimal by dividing by 100)
- n is 1, since the interest is compounded annually
- t is 6 years
Substituting these values into the formula gives us:
A = $4000(1 + 0.03/1)1 ⩽6
A = $4000(1 + 0.03)6
A = $4000(1.03)6
Calculating this:
A = $4000 ⩽7 1.194052
A = $4776.21
The balance after 6 years, rounded to the nearest cent, is $4776.21.
Therefore, none of the given options are correct.