Answer :
The present value of ordinary annuity which has payments of $2200 per year for 18 years at 9% compounded annually is $19,286.67.
What is Ordinary Annuity?
The present value of an ordinary or a regular annuity involving a fixed stream of income is derived by discounting all the future receipts or payments attached to the annuity at a particular rate that is known as a discount rate.
What is present value of an annuity?
The present value of an annuity is the current cash value of all future payments, impacted by the annuity’s rate of return or discount rate.
The formula used to calculate present value of annuity is
P = PMT x [tex]\frac{1 - (\frac{1}{(1+r)^n})}{r}[/tex] where
P = present value of annuity
PMT = dollar amount of each annuity payment
r = discount rate or interest rate
n = number of periods in which payment will be made
According to the given question:
PMT = $2200
r = 9% represented as 0.09
n = 18 years
Now, present value of an ordinary annuity
P = PMT x [tex]\frac{1 - (\frac{1}{(1+r)^n})}{r}\\[/tex]
= 2200 x [tex]\frac{1 - (\frac{1}{(1+0.09)^(18)})}{0.09}\\[/tex]
= 2200 x 8.767
= $19,286.67
Therefore the present value of ordinary annuity is $19,286.67
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