Final answer:
The balance in an account with a $4,000 deposit at a 3.4% interest rate compounded annually for three years will be $4,422.20.
Step-by-step explanation:
The balance in an account after depositing $4,000 at an interest rate of 3.4% compounded annually for three years can be determined using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for
For this problem:
P = $4,000
r = 0.034 (3.4% as a decimal)
n = 1 (since interest is compounded annually)
t = 3
Now substitute these values into the formula to calculate the balance:
A = 4000(1 + 0.034/1)^(1*3)
= 4000(1 + 0.034)^3
= 4000(1.034)^3
= 4000(1.10555124)
= $4,422.20
Therefore, the balance after three years will be $4,422.20.