Answer to Question #287524 in Financial Math for LilI

Question

What is the present value of an annuity if the size of each payment is Birr 100 payable at the 

end of each quarter for 2 years and the interest rate is 8% compounded quarterly?

Answer 1

Solution:

Given, P=100, t=2, n=4 (as quarters), r=8% compounded quarterly.

We know that, $PV=P\times\dfrac{1-(1+\frac rn)^{-nt}}{\frac rn}$

Putting given values,

$PV=100\times\dfrac{1-(1+\frac {0.08}4)^{-8}}{\frac {0.08}4} \\=100\times\dfrac{0.1465096}{0.02} \\=732.548\ birr$