Find the future value of an annuity due of $100 each quarter for 2½ years at 11%, compounded quarterly.
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+....+Rn-1)
=$100(R^n - 1)/(R-1)
=$100(1.0275^10 -1)/(1.0275-1)
=$1133.28
the answer was wrong according to my instructor :(
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.
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
To find the future value of an annuity due, you can use the formula:
Future Value = P * [(1 + r)^n - 1] / r
where:
P = periodic payment
r = interest rate per period
n = number of periods
In this case, the periodic payment (P) is $100, the interest rate per period (r) is 11% or 0.11, and the number of periods (n) is 2½ years or 10 quarters.
First, we need to calculate the future value of the annuity if it were an ordinary annuity (not due). We can use the formula:
Future Value of Ordinary Annuity = P * [(1 + r)^n - 1] / r
Future Value of Ordinary Annuity = $100 * [(1 + 0.11)^10 - 1] / 0.11
Calculating this, we get:
Future Value of Ordinary Annuity = $100 * [(1.11)^10 - 1] / 0.11
≈ $100 * (2.853 - 1) / 0.11
≈ $100 * 1.853 / 0.11
≈ $100 * 16.846
≈ $1,684.60
Now, to find the future value of an annuity due, we need to adjust the amount we calculated for the ordinary annuity. Since an annuity due payments are made at the beginning of each period, we multiply the calculated amount by (1 + r).
Future Value of Annuity Due = Future Value of Ordinary Annuity * (1 + r)
Future Value of Annuity Due = $1,684.60 * (1 + 0.11)
= $1,684.60 * 1.11
≈ $1,869.91
Therefore, the future value of the annuity due is approximately $1,869.91.