Find future value of a bank account after 3 years if present value is $4000 earns 4.6% p.a interest comppoundly quarterly

To find the future value of a bank account after 3 years with quarterly compounding interest, we can use the formula for compound interest:

A = P\left(1 + \frac{r}{n}\right)^{nt}

Where:
A = future value
P = present value
r = interest rate (as decimal)
n = number of compounding periods per year
t = number of years

Given: P = $4000, r = 4.6% = 0.046, n = 4 (quarterly compounding), and t = 3 years.

Plug the values into the formula:
A = 4000\left(1 + \frac{0.046}{4}\right)^{4 \cdot 3}

Simplify the exponent:
A = 4000\left(1 + 0.0115\right)^{12}

Calculate the value inside parentheses:
A = 4000(1.0115)^{12}

Evaluate the exponent and multiply:
A\approx4588.29

Answer: The future value of the bank account after 3 years will be approximately $4588.29.