$11,000, invested for 9 years at 3% compounded quarterly.
P = Po(1+r)^n
Po = $11,000
r = (3%/4)/100% = 0.0075 = Quarterly
% rate expressed as a decimal.
n = 4comp./yr. * 9yrs. = 36 Compounding
periods.
Plug the above values into the given Eq
and solve for P(principal).
To calculate the future value of an investment compounded quarterly, you can use the formula:
FV = P(1 + r/n)^(nt)
Where:
FV is the future value
P is the principal amount (initial investment)
r is the annual interest rate (as a decimal)
n is the number of compounding periods per year
t is the number of years
Given:
P = $11,000
r = 3% or 0.03 (as a decimal)
n = 4 (quarterly compounding)
t = 9 years
Let's substitute the values into the formula and calculate it:
FV = 11000(1 + 0.03/4)^(4*9)
First, we simplify the calculation within parentheses:
FV = 11000(1 + 0.0075)^(4*9)
= 11000(1.0075)^36
Next, raise 1.0075 to the power of 36:
FV = 11000(1.337635...)
Finally, multiply $11,000 by the result:
FV ≈ $14,713.99
Therefore, if $11,000 is invested for 9 years at a 3% interest rate compounded quarterly, the future value will be approximately $14,713.99.