Question

Regarding the present value of an annuity, the present value of a nine year ordinary annuity will always be worth less compared to the present value of a nine year annuity due.

i think it is true, please verify i am correct!

Answer 1

You are correct! the present value of a nine year ordinary annuity will always be worth less compared to the present value of a nine year annuity due.

Ordinary annuity is paid at the end of the year. Annuity due is paid at the beginning of the year.

For exampale:

Ordinary annuity:

Number of periods = 9

Rate = 10%

Annuity payment = $1,000

Present value = Annuity * [1 - 1 / (1 + r)ⁿ] / r

Present value = 1,000 * [1 - 1 / (1 + 0.1)⁹] / 0.1

Present value = 1,000 * 5.759024

Present value of ordinary annuity = $5.759

annuity due:

Number of periods = 9

Rate = 10%

Annuity payment = $1,000

Present value =(1 + r) * Annuity * [1 - 1 / (1 + r)ⁿ] / r

Present value = (1 + 0.1) * 1,000 * [1 - 1 / (1 + 0.1)⁹] / 0.1

Present value = (1.1) * 1,000 * 5.759024

Present value of annuity due = $6,335

Therefore, annuity due has a greater present value.