Find the balance in the account after the given period.
$ 4,700 deposit earning 3.9 % compounded monthly, after 3 years.
To find the balance in the account after 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the future balance
P = the principal amount deposited
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, P = $4,700, r = 0.039 (3.9% expressed as a decimal), n = 12 (monthly compounding), and t = 3 years.
Substituting the values into the formula, we have:
A = 4700(1 + 0.039/12)^(12*3)
Simplifying the equation inside the parentheses:
A = 4700(1 + 0.00325)^(36)
A = 4700(1.00325)^(36)
Using a calculator, we can find that (1.00325)^36 ≈ 1.122887
So the balance in the account after 3 years is:
A ≈ $4,700 * 1.122887
A ≈ $5,279.79
Therefore, the balance in the account after the given period is approximately $5,279.79.