Question

Consider two identical annuities with same positive discount rate and number of payments. Annuity A pays at the end of each year, while annuity B pays at the beginning of each year.

Which of the following statements is correct?

		Present value of annuity B < Present value of annuity A
		Future value of annuity B > future value of annuity A
		Future value of annuity B < Future value of annuity A
		They both have the same present value
		Present value of annuity A > Present value of annuity B

Answer 1

For end of year payments;

Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

while for beginning of year payments;

Present value of annuity due=Present value of annuity*(1+rate)

Similarly:

For end of year payments;

Future value of annuity=Annuity[(1+rate)^time period-1]/rate

while for beginning of year payments;

Future value of annuity due=Future value of annuity*(1+rate)

Hence present value of annuity B>present value of annuity A

and future value of annuity B>future value of annuity A

Hence the correct option is:

Future value of annuity B > future value of annuity A