Determine the future value of an annuity due into which quarterly deposits of $450 are made for nine years if the annuity pays 10% compounded quarterly.
quarterly rate = .10/4 = .025
number of quarter years in 9 yrs = 36
Future value = 450((1.025^36 - 1)/.025
= $25785.64
Thanks Reiny
To determine the future value of an annuity due, we can use the formula:
Future Value = P * (((1 + r/n)^(n*t) - 1) / (r/n)) * (1 + r/n)
Where:
P is the periodic payment (quarterly deposit)
r is the interest rate per period
n is the number of compounding periods per year
t is the number of years
In this case:
P = $450 (quarterly deposits)
r = 10% (interest rate per year) = 0.10
n = 4 (quarterly compounding periods per year)
t = 9 (number of years)
Substituting the values into the formula:
Future Value = $450 * (((1 + 0.10/4)^(4*9) - 1) / (0.10/4)) * (1 + 0.10/4)
Now, let's calculate the future value.