Question

Present value of an annuity???Using the values? below, answer the questions that follow.

Amount of annuity= $8,500 Interest rate= 7% Deposit period? (years)= 7

a.??Calculate the present value of the? annuity, assuming that it is: ?

(1) An ordinary annuity. ?

(2) An annuity due.

b.??Compare your findings in parts a?(1) and a?(2). All else being? identical, which type of

annuity -ordinary or annuity due- yields a higher present? value? Explain why.

Answer 1

1) Present value of an ordinary annuity is computed as follows -

where, A = amount of annuity, r = interest rate, n = no. of years, PV = Present value

or, PV = $45,808.96

2) Present value of an annuity due is computed as follows -

or, PV = $49,015.59

The value of the annuity due is higher because annuities are paid / received one period earlier in case of an annuity due. Since, the amount of annuities are received / paid earlier, they get discounted for lesser period than in case of ordinary annuity.