Question

Why we cannot use different compounding periods when comparing alternatives in the present or future worth methods? Give an example of how different compounding periods will affect the selection of an alternative.

Answer 1

Different compounding periods will impact the values of present worth and future worth analysis and make them incomparable

For instance

Consider an annuity of $100 for 3 years. The rate of interest is 12%

With annual compounding the value of

Present value will be Annuity*(1-1/(1+rate)^number of terms)/rate

= 100*(1-1/1.12^3)/0.12

=$ 240.18

Future Value of annuity = A*((1+rate)^number of periods-1)/rate

= 100*((1.12^3-1)/0.12)

=337.44

With semi annual compounding

Present value will be Annuity*(1-1/(1+rate)^number of terms)/rate

= 100*(1-1/1.06^6)/0.06

=$ 490.73

Future Value of annuity = A*((1+rate)^number of periods-1)/rate

= 100*((1.06^6-1)/0.06)

=697.53

Thus we see that the PV and FV are different with different compounding periods.HIgher the compounding higehr will be the PV and FV and this option will be selected in case of receipts. In case of payments, select the option with lesser compounding