Find the future value of an annuity due of $100 each quarter for 2½ years at 11%, compounded quarterly.

Answer 1

11% compounded quarterly is equivalent to 11/4% per quarter (period).
R=1+0.11/4=1.0275
$100 per quarter for 2 1/2 years
is $100 per period for 10 periods.

Future value
=$100(1+R+R²+R³+....+R^n-1)
=$100(R^n - 1)/(R-1)
=$100(1.0275^10 -1)/(1.0275-1)
=$1133.28

Answer 2

the answer was wrong according to my instructor :(

Answer 3

Are annuities paid in advance or paid at the end of the quarter?

Is the payment $100 per quarter?

If it is paid at the beginning of the quarter, then the future value would be slightly more.

Ask the "instructor" to show you an example to clarify the above questions. I assume you "instructor" is a computer application. Actually, most of the time, the examples given by the computer applications are very similar to your problem.

Answer 4

Sorry, this is an "annuity due" problem, where the payments are made in advance.

$100 paid quarterly in advance for 2 1/2 years at 11% interest.
n=10 quarters
R=1+0.11/4=1.0275 (compounded quarterly)

Future value
= $100*(R+R²+...R^n)
= $100*R*(1+R+....+R^(n-1))
Use the normal formula for annuity
= $100R(R^n-1)/(R-1)
= $100*1.0275(1.0275^10-1)/(1.0275-1)
= $1164.44