Find the present value of $200 due in the future under each of these conditions:

Question

Find the present value of $200 due in the future under each of these conditions:

7% nominal rate, semiannual compounding, discounted back 5 years. Round your answer to the nearest cent.
$  

7% nominal rate, quarterly compounding, discounted back 5 years. Round your answer to the nearest cent.
$  

7% nominal rate, monthly compounding, discounted back 1 year. Round your answer to the nearest cent.
$  

Why do the differences in the PVs occur?
-Select-The present values decline as the discounting periods per year increaseThe present values decline as the discounting periods per year decreaseThe present values increase as the discounting periods per year increaseThe present values are not affected by changes in the number of discounting periods per yearThe present values are positively related to the number of discounting periods per yearItem 4

Explanation / Answer

1. Rate per period = 7%/2 = 3.5%

No of periods = 5*2 = 10 periods

Present value = 200/(1+3.5%)^10 = 141.78

2. Rate per period = 7%/4 = 1.75%

No of periods = 5*4 = 20 periods

Present value = 200/(1+1.75%)^20 = 141.36

3. Rate per period = 7%/12

No of periods = 1*12 = 12 periods

Present value = 200/(1+7%/12)^12 = 186.52

4. The present values decline as the discounting periods per year increase

Hope this helped ! Let me know in case of any queries.

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