Problem 5-24 Present value for various discounting periods Find the present valu

ID: 2650124 • Letter: P

Question

Problem 5-24
Present value for various discounting periods

Find the present value of $600 due in the future under each of these conditions:

16% nominal rate, semiannual compounding, discounted back 4 years. Round your answer to the nearest cent.
$

16% nominal rate, quarterly compounding, discounted back 4 years. Round your answer to the nearest cent.
$

16% nominal rate, monthly compounding, discounted back 1 year. Round your answer to the nearest cent.
$

Why do the differences in the PVs occur?

Answer:

Calculation of Present value :

Present value = Future value / (1+r)^n

Case 1:

Future value =$600

r= rate of interest =16% =0.16 /2 =0.08 (Semiannual)

n= Number of semiannual =4 *2 =8

Hence Present value =600 / (1+0.08)^8

= 600 /1.85093

=$324.16

Case 2:

Future value =$600

r= rate of interest =16% =0.16 /4 =0.04 (Quarterly)

n= Number of quarters =4 *4 =16

Hence Present value =600 / (1+0.04)^16

= 600 /1.87298

=$320.35

Case 3:

Future value =$600

r= rate of interest =16% =0.16 /12 =0.013333333 (monthly)

n= Number of months =1 *12 =12

Hence Present value =600 / (1+0.01333333)^12

= 600 /1.17227

=$511.83

Differences in PV occurred due to compounding differences.

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