Question

Assuming the same interest rate, which has the greater present value: i) an asset that generates a certain amount of revenue at the beginning of every year for 5 years or ii) an asset that generates a certain amount of revenue at the end of every year for 5 years ? Why? (Please show examples for both )

Answer 1

Present value of an ordinary annuity = C*[(1-(1/(1+r)^t))/r]
where C is the annuity payment that is 100.
r is the interest rate that is .08.
t is the time period in years that is 5.
Present value of an ordinary annuity = 100*[(1-(1/(1.08)^5))/.08]
Present value of an ordinary annuity = 100*[(1-(1/(1.469328))/.08]
Present value of an ordinary annuity = 100*[(1-(.680583))/.08]
Present value of an ordinary annuity = 100*[(.319417)/.08]
Present value of an ordinary annuity = 100*[3.99271]
Present value of an ordinary annuity = 399.271.
An ordinary annuity is an annuity that makes annuity payments at the end of every year
for 5 years. The ordinary annuity has a present value of $399.27.
Present value of an annuity due = Present value of an ordinary annuity*(1+r)
r is the interest rate that is .08.
Present value of an annuity due = 399.27*(1+.08)
Present value of an annuity due = 431.21.
An annuity due is an annuity that makes annuity payments at the beginning of
every year for 5 years. The present value of the annuity due is $431.21.
Based on the example, (at the same interest rate) the present value of the annuity due is greater
than the present value of an ordinary annuity.