Question

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

12% nominal rate, semiannual compounding, discounted back 6 years. Do not round intermediate calculations. Round your answer to the nearest cent.

12% nominal rate, quarterly compounding, discounted back 6 years. Do not round intermediate calculations. Round your answer to the nearest cent.

12% nominal rate, monthly compounding, discounted back 1 year. Do not round intermediate calculations. Round your answer to the nearest cent.

Why do the differences in the PVs occur?

Answer 1

Solution

Present value of a cashflow=future cashflow/(1+r)^n

where

r-discount rate per period

n-number of discounting periods

Now calculating one by one

12% nominal rate, semiannual compounding, discounted back 6 years

Here

n-6*2=12

r=12/2=6% semiannual

Putting values in formula

Present value =200/(1+.06)^12=$99.39

12% nominal rate, quarterly compounding, discounted back 6 years

Here

n-6*4=24

r=12/4=3% quaterly

Putting values in formula

Present value =200/(1+.03)^24=$98.39

12% nominal rate, monthly compounding, discounted back 1 year

Here

n-1*12=12

r=12/12=1% monthly

Putting values in formula

Present value =200/(1+.01)^12=$177.49

The difference in PV occur in first 2 cases due to number of compounding periods .More the number of compounding periods in a year more is the effective rate of discounting and lesser the present value.In the third case the tenure of discounting is lesser ,thus the present value is more

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