Question

Find the present value of an ordinary annuity which has payments of $19157.64 per year for 24 years at 12.34 % compounded quarterly.
Select one:

a.
$ 578359.94

b.
$ 567439.11

c.
$ 543712.35

d.
$ 587394.59

Answer 1

Given:

An ordinary annuity that has payments of $19157.64 per year for 24 years at 12.34 % compounded quarterly.

To Find:

Present value

Solution:

To find the present value of an ordinary annuity we use a formula i.e.

                         $PV_{ordinary annuity}=C[\frac{1-(1+i)^{-n}}{i}]$

where,

           $C$= Payments per annum

           $i$=rate of interest

           $n$=time period

So now putting all the values in the formula and it will be slightly changed as the interest is being compounded quarterly which will affect the rate of interest and time period

$C=19157.64\\i=\frac{0.1234}{4}=0.03085\\n=24*4=96$

Therefore,

$PV_{OA}=19157.64[\frac{1-(1+0.03085)^{-96}}{0.03085} ]\\=19157.64*\frac{0.94589}{0.03085}\\=19157.64*30.66111\\=587394.50738$

the value is approximately equal to option (d)

Hence, the correct answer is option(d) $587394.59