Question

Problem 2.9 An annuity immediate has semi-annual payments of 1,000 for 25 years at a rate of 6%, convertible quarterly. Find the present value.

Answer 1

The frequency of compounding and frequency of annuity pay outs is different in this case. Hence, one needs to convert the quarterly compounding rate to an equivalent half-yearly compounding rate so as to match the half-yearly annuity pay out frequency

Annual Percentage Rate (APR) = 6 %

Quarterly Rate = (6 / 4) = 1.5 %

Equivalent Semi-Annual Rate = (1.015)^(2) - 1 = 0.030225 or 3.0225 %

Annuity Payout = $ 1000 and Tenure = 25 years or 50 half-years

Therefore, Present Value = 1000 x (1/0.030225) x [1-{1/(1.030225)^(50)}] x (1.030225) = $ 26394.57