Question

Present Value for Various Compounding Periods

Find the present value of $500 due in the future under each of the following conditions. Do not round intermediate calculations. Round your answers to the nearest cent.

1. 4% nominal rate, semiannual compounding, discounted back 5 years
   $  
   
2. 4% nominal rate, quarterly compounding, discounted back 5 years
   $  
   
3. 4% nominal rate, monthly compounding, discounted back 1 year
   $  

Answer 1

a)

Future Value (FV)	$500
Interest Rate - Semi-annual (i)	4percent / 2 = 2 percent (half-yearly)
Number of Periods (n)	5 years x 2 = 10 periods

According to Problem:

$\dpi{100} \fn_cm \mathrm{PV = FV / (1 + i)^{n}}$

$\dpi{100} \fn_cm \mathrm{PV = 500 / (1 + 2/100)^{10}}$

$\dpi{100} \fn_cm \mathrm{PV = 410.17}$

Therefore, PRESENT VALUE = $410.17

b)

Future Value (FV)	$500
Interest Rate – Quarterly Compounded (i)	4percent / 4 = 1 percent (per quarter)
Number of Periods (n)	5 years x 4 = 20 periods

According to Problem:

$\dpi{100} \fn_cm \mathrm{PV = FV / (1 + i)^{n}}$

$\dpi{100} \fn_cm \mathrm{PV = 500 / (1 + 1/100)^{20}}$

$\dpi{100} \fn_cm \mathrm{PV = 409.77}$

Therefore, PRESENT VALUE = $409.77

c)

Future Value (FV)	$500
Interest Rate – monthly compounded (i)	4percent / 12 = 0.33% percent (per month)
Number of Periods (n)	1 year x 12 = 12 periods

According to Problem:

$\dpi{100} \fn_cm \mathrm{PV = FV / (1 + i)^{n}}$

$\dpi{100} \fn_cm \mathrm{PV = 500 / (1 + 0.33/100)^{12}}$

$\dpi{100} \fn_cm \mathrm{PV = 480.62}$

Therefore, PRESENT VALUE = $480.62