$11,000, invested for 9 years at 3% compounded quarterly.
11000(1+.03/4)^(4*9)
To calculate the future value of an investment compounded quarterly, you can use the formula:
FV = PV * (1 + r/n)^(n*t)
Where:
FV = Future Value
PV = Present Value (initial investment)
r = Interest rate per period (in decimal form)
n = Number of compounding periods per year
t = Number of years
In this case:
PV = $11,000
r = 3% = 0.03 (as a decimal)
n = 4 (quarterly compounding)
t = 9 years
Let's plug in the values and calculate the future value:
FV = $11,000 * (1 + 0.03/4)^(4*9)
Calculating the exponent:
(1 + 0.03/4)^(4*9) = (1 + 0.0075)^36
(1 + 0.0075) = 1.0075 (rounded)
Now, let's continue with the calculation:
FV = $11,000 * (1.0075)^36
Using a calculator, we get:
FV ≈ $14,485.82
Therefore, when $11,000 is invested for 9 years at a 3% interest rate compounded quarterly, the future value will be approximately $14,485.82.