Question

Find the present values of these ordinary annuities. Discounting occurs once a year. Do not round intermediate calculations. Round your answers to the nearest cent.

1. $900 per year for 14 years at 4%.

   $  

2. $450 per year for 7 years at 2%.

   $  

3. $600 per year for 7 years at 0%.

   $  

4. Rework previous parts assuming they are annuities due.

   Present value of $900 per year for 14 years at 4%: $  

   Present value of $450 per year for 7 years at 2%: $  

   Present value of $600 per year for 7 years at 0%: $

Answer 1

The present value is computed as follows:

Present value = Annual amount x [ (1 – 1 / (1 + r)ⁿ) / r ]

a. The amount will be as follows:

= $ 900 x [ (1 - 1 / (1 + 0.04)¹⁴ ) / 0.04 ]

= $ 900 x 10.56312293

= $ 9,506.81

b. The amount will be as follows:

= $ 450 x [ (1 - 1 / (1 + 0.02)⁷ ) / 0.02 ]

= $ 450 x 6.471991069

= $ 2,912.40

c. The amount will be as follows:

= Annual amount x number of years

= $ 600 x 7

= $ 4,200

d. The annuity due is computed as follows:

Present value = Annual amount x [ (1 – 1 / (1 + r)ⁿ) / r ] x (1 + r)

The amount will be as follows:

= $ 900 x [ (1 - 1 / (1 + 0.04)¹⁴ ) / 0.04 ] x 1.04

= $ 900 x 10.56312293 x 1.04

= $ 9,887.08

The amount will be as follows:

= $ 450 x [ (1 - 1 / (1 + 0.02)⁷ ) / 0.02 ] x 1.02

= $ 450 x 6.471991069 x 1.02

= $ 2,970.64

The amount will be as follows:

= Annual amount x number of years

= $ 600 x 7

= $ 4,200

Feel free to ask in case of any query relating to this question