Question

4. What is the present value of an annuity due consisting of 5 annual payments of $4,000 with an interest rate of 9% p.a.

1. $16,959
2. $16,006  
3. $19,558
4. $18,765
5. None of the above

Answer 1

Present Value of an Annuity Due

Present Value of an Annuity Due is calculated by using the following formula

Annual Payment (P) = $4,000 per year

Annual Interest Rate (r) = 9% per year

Number of years (n) = 5 Years

Present Value of an Annuity Due = (1 + r) x P x [{1 - (1 / (1 + r) n} / r]

= (1 + 0.09) x $4,000 x [{1 - (1 / (1 + 0.09)⁵} / 0.09]

= 1.09 x $4,000 x [{1 - (1 / 1 1.53862)} / 0.09]

= 1.09 x $4,000 x [(1 - 0.64993) / 0.09]

= 1.09 x $4,000 x [0.35007 / 0.09]

= 1.09 x $4,000 x 3.88965

= $16,959

“Hence, the Present Value of the Annuity Due = $16,959”