Question

1. Find the present value of $800 due in the future under each of these conditions:

1. 5% nominal rate, semiannual compounding, discounted back 5 years. Do not round intermediate calculations. Round your answer to the nearest cent.
   $  

2. 5% nominal rate, quarterly compounding, discounted back 5 years. Do not round intermediate calculations. Round your answer to the nearest cent.
   $  

3. 5% nominal rate, monthly compounding, discounted back 1 year. Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

a)

Rate = 5% / 2 = 2.5%

Number of periods = 5 * 2 = 10

Present value = Future value / (1 + r)ⁿ

Present value = 800 / (1 + 0.025)¹⁰

Present value = 800 / 1.280085

Present value = $624.96

b)

Rate = 5% / 4 = 1.25%

Number of periods = 5 * 4 = 20

Present value = Future value / (1 + r)ⁿ

Present value = 800 / (1 + 0.0125)²⁰

Present value = 800 / 1.282037

Present value = $624.01

c)

Rate = 5% / 12 = 0.4167%

Number of periods = 1 * 12 = 12

Present value = Future value / (1 + r)ⁿ

Present value = 800 / (1 + 0.004167)¹²

Present value = 800 / 1.0511661

Present value = $761.06