Final answer:
To calculate the balance after 4 years in an account with $3000 initial deposit and 6% interest compounded annually, use the compound interest formula A = P(1 + r/n)^(nt). The balance would be approximately $3787.43.
Step-by-step explanation:
You deposit $3000 in an account that pays 6% annual interest. To find the balance after 4 years when the interest is compounded, you can use the compound interest formula:
A = P(1 + r/n)^(nt)
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 number of years the money is invested or borrowed for.
In this scenario, P = $3000, r = 0.06 (since 6% = 6/100 = 0.06), n = 1 (compounded annually means once per year), and t = 4 years.
A = $3000(1 + 0.06/1)^(1*4)
A = $3000(1 + 0.06)^4
A = $3000(1.06)^4
Using a calculator:
A ≈ $3000 * 1.262477
A ≈ $3787.43
After 4 years, the balance in the account would be approximately $3787.43.