Find the present value of an annuity if $1,400.00 is paid to you at the end of each quarter for 3 years, if interest is earned at a rate of 6%, compounded quarterly.
To find the present value of an annuity, we can use the formula:
PV = PMT * ((1 - (1 + r)^(-n)) / r)
Where:
PV = Present Value (or the sum of all the payments)
PMT = Payment per period ($1,400.00 in this case)
r = Interest rate per period (6% / 4 = 1.5% or 0.015)
n = Number of periods (4 quarters in a year * 3 years = 12 quarters)
Let's calculate:
PV = $1,400.00 * ((1 - (1 + 0.015)^(-12)) / 0.015)
PV = $1,400.00 * ((1 - 0.8486073059) / 0.015)
PV = $1,400.00 * (0.1513926941 / 0.015)
PV = $1,400.00 * 10.0928462741
PV = $14,129.99
Therefore, the present value of the annuity is $14,129.99.