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. $400 per year for 14 years at 8%.

   $  

2. $200 per year for 7 years at 4%.

   $  

3. $700 per year for 12 years at 0%.

   $  

4. Rework previous parts assuming they are annuities due.

   Present value of $400 per year for 14 years at 8%: $  

   Present value of $200 per year for 7 years at 4%: $  

   Present value of $700 per year for 12 years at 0%: $  

Answer 1

a)

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

Present value = 400 * [1 - 1 / (1 + 0.08)¹⁴] / 0.08

Present value = 400 * 8.244237

Present value = $3,297.7

b)

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

Present value = 200 * [1 - 1 / (1 + 0.04)⁷] / 0.04

Present value = 200 * 6.002055

Present value = $1,200.4

c)

Present value = Annuity * number of periods

Present value = 700 * 12

Present value = $8,400

d)

Annuity due:

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

Present value = (1 + 0.08) *400 * [1 - 1 / (1 + 0.08)¹⁴] / 0.08

Present value = 1.08 * 400 * 8.244237

Present value = $3,461.5

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

Present value = (1 + 0.04) * 200 * [1 - 1 / (1 + 0.04)⁷] / 0.04

Present value = 1.04 * 200 * 6.002055

Present value = $1,248.4

Present value = Annuity * number of periods

Present value = 700 * 12

Present value = $8,400