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 differences in the PVs occur?

Answer 1

Present Value:
PV = FV / (1+r)^n
Where r is Int rate per period
n - No. of periods

Nominal interest rate = 15 %
Part a.

Particulars	Amount
future Value	$                700.00
Int Rate	7.5000%
Periods	8

Int rate per period = 15 % / 2 = 7.5 %
n - No. of periods = 4 years * 2 = 8

Present Value = Future Value / ( 1 + r )^n
= $ 700 / ( 1 + 0.075 ) ^ 8
= $ 700 / ( 1.075 ) ^ 8
= $ 700 / 1.7835
= $ 392.49

Part b.

Particulars	Amount
future Value	$                700.00
Int Rate	3.7500%
Periods	16

Int rate per period = 15 % / 4 = 3.75 %
n - No. of periods = 4 years * 4 quarters = 16

Present Value = Future Value / ( 1 + r )^n
= $ 700 / ( 1 + 0.0375 ) ^ 16
= $ 700 / ( 1.0375 ) ^ 16
= $ 700 / 1.8022
= $ 388.41

Part c.

Particulars	Amount
future Value	$                700.00
Int Rate	1.2500%
Periods	48

Int rate per period = 15 % / 12 = 1.25 %
n - No. of periods = 4 years * 12months = 48

Present Value = Future Value / ( 1 + r )^n
= $ 700 / ( 1 + 0.0125 ) ^ 48
= $ 700 / ( 1.0125 ) ^ 48
= $ 700 / 1.8154
= $ 385.6

Part d.

As the number of compounding periods increases the effective annual interest rate increases so does the future value increases And present value (PVs) Decreases. Quarterly compounding produces higher returns than semi-annual compounding, monthly compounding more than quarterly,

please comment oif any furtehr assistance is required.