Question

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

1. 6% nominal rate, semiannual compounding, discounted back 8 years. Do not round intermediate calculations. Round your answer to the nearest cent.
   $   

2. 6% nominal rate, quarterly compounding, discounted back 8 years. Do not round intermediate calculations. Round your answer to the nearest cent.
   $   

3. 6% nominal rate, monthly compounding, discounted back 1 year. Do not round intermediate calculations. Round your answer to the nearest cent.
   $   

4. Why do the differences in the PVs occur?

Answer 1

a. Present value = amount / (1 + Semi annual Interest)^(Years * compounding per year)

Present value = 600 / (1 + 0.03)^(8 * 2)

Present value = 600 / 1.03^16

Present value = 600 / 1.6047

Present value = $373.90

b. Present value = amount / (1 + Quarterly Interest)^(Years * compounding per year)

Present value = 600 / (1 + 0.015)^(8 * 4)

Present value = 600 / 1.015^32

Present value = 600 / 1.6103

Present value = $372.60

c. Present value = amount / (1 + Monthly Interest)^(Years * compounding per year)

Present value = 600 / (1 + 0.005)^(1 * 12)

Present value = 600 / 1.005^12

Present value = 600 / 1.0617

Present value = $565.14

d. the difference between present occurred due to compounding of the rate which makes present value to decrease when compounding increases and increases when compounding decreases