Find the future value of an ordinary annuity of $100 paid at the end of each quarter for 6 years, if interest is earned at a rate of 6%, compounded quarterly.
To find the future value of an ordinary annuity, we use the formula:
FV = P * ((1 + r/q)^(n*q) - 1) / (r/q)
Where:
FV = future value
P = payment amount per period
r = annual interest rate (as a decimal)
q = number of compounding periods per year
n = number of years
In this case, P = $100, r = 6% = 0.06, q = 4 (quarterly compounding), and n = 6.
Plugging these values into the formula, we get:
FV = $100 * ((1 + 0.06/4)^(6*4) - 1) / (0.06/4)
Simplifying further:
FV = $100 * ((1 + 0.015)^24 - 1) / 0.015
FV = $100 * (1.015^24 - 1) / 0.015
FV = $100 * (1.446007 - 1) / 0.015
FV = $96.40046 / 0.015
FV = $6,426.70
So, the future value of the annuity is $6,426.70.