Question

Find the present value of $700 due in the future under each of these conditions:

1. 15% nominal rate, semiannual compounding, discounted back 4 years. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

2. 15% nominal rate, quarterly compounding, discounted back 4 years. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

3. 15% nominal rate, monthly compounding, discounted back 1 year. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

4. Why do the difference in the PV's Occur?

Answer 1

Answer (a):

FV = $700

Semiannual interest rate = 15% / 2 = 7.5%

Number of semiannual periods = 4 * 2 = 8

PV = FV /(1 + Periodic interest rate) ^{Number of periods}

= 700 / (1 + 7.5%) ⁸

= $392.49

Present value = $392.49

Answer (b):

FV = $700

Quarterly interest rate = 15% / 4 = 3.75%

Number of quarters = 4 * 4 = 16

PV = FV / (1 + Periodic interest rate) ^{Number of periods}

= 700 / (1 + 3.75%) ¹⁶

= $388.41

Present value = $388.41

Answer (c):

FV = $700

Monthly interest rate = 15% / 12 = 1.25%

Number of months = 1 * 12 = 12

PV = FV / (1 + Periodic interest rate) ^{Number of periods}

= 700 / (1 + 1.25%) ¹²

= $603.06

Present value = $603.06

Answer (d):

Reasons of difference in PV:

1. When we increase number of compounding periods effective annual rate increases which reduces the discounting factor we apply to future cash flow. This results in reduction in PV.

2. If the discounting period reduces (in case of C above), discounting factor applied increases.