Find the present value of an annuitydue of 1600 per annum pa

Find the present value of an annuity-due of $1600 per annum payable quarterly for 5 years if i⁽¹²⁾ = .06.

Here, we first calculate the Present Value of an Ordinary Annuity, using the formula

PVoa = PMT [(1 - (1 / (1 + i)ⁿ)) / i]

Here,

So, PV_0a= $400[(1-1/(1+0.015)²⁰0/0.015]

=$400[(1-1/1.346855)/0.015]

=$400[0.25753/0.015]

=$400(17.16864)

=&6867.455

Now, we calculalte the present value of an annity-due using the formula,

PVad = PVoa (1+i)

Where,

So,

PVad= $6867.455(1+0.015)

=$6867.455(1.015)

= $6970.467

Hence, the answer is $6970.47