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?
Explanation / Answer
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.