Determine the PG factor for 5 years at an effective interest

Determine the P/G factor for 5 years at an effective interest rate of 6% per year, compounded semiannually.

Solution

Semi-annual interest rate (r) = 6%/12 = 0.5%

Number of compounding periods (N) = 5 x 2 = 10

P/G(r%, N) = [(1 + r)^N - (r x N) - 1] / [r² x (1 + r)^N]

P/G(0.5%, 10) = [(1 + 0.005)¹⁰ - (0.005 x 10) - 1] / [(0.005)² x (1 + 0.005)¹⁰]

= [(1.005)¹⁰ - 0.05 - 1] / [0.000025 x (1.005)¹⁰]

= (1.0511 - 1.05) / (0.000025 x 1.0511)

= 0.0011 / 0.0000262775

= 41.8609