Final answer:
To calculate the balance after 1 year for a deposit of $3,900 earning 4.5% interest compounded monthly, the compound interest formula is used, resulting in an approximate balance of $4,082.72.
Step-by-step explanation:
To find the balance in the account after one year with an initial deposit of $3,900 earning 4.5% interest compounded monthly, we will use the compound interest formula:
A = P(1 + r/n)nt
Where:
P is the principal amount ($3,900)
r is the annual interest rate (4.5% or 0.045)
n is the number of times interest is compounded per year (12 for monthly)
t is the time the money is invested for in years (1 year)
Plugging these values into the formula we get:
A = $3,900(1 + 0.045/12)12*1
Calculating the values:
A = $3,900(1 + 0.00375)12 = $3,900(1.00375)12
A = $3,900 * 1.04685 ≈ $4,082.72 when rounded to the nearest cent
Therefore, the balance after one year will be approximately $4,082.72.