Question

2. You deposit $1000. How much will you have under each of the following conditions?

a) 8 percent compounded semi-annually for two years

b) 8 percent compounded quarterly for two years

c) 8 percent compounded monthly for two years

Answer 1

Solution:			Value at end 2nd year
a.	8 percent compounded semi-annually for two years		$1,169.86
b.	8 percent compounded quarterly for two years		$1,171.66
c.	8 percent compounded monthly for two years		$1,172.89
Working Notes:
Notes:	Under each of the condition, the account earn 8%, but compounded at different frequency during a year, so value at end of two years period will be different as follows:
a.	8 percent compounded semi-annually for two years
	8 percent compounded semi-annually for two years, means twice compounded in a year for semi annual compounding , so in two years it will compounded for 4 times. Rate per semi annual be different as rate at which it will compounded semi annually = (annual rate/2) as for semi annual compounding it will be compounding twice.
	Future value = Ending balance in the account after 2 year =??
	Present value = $1000 deposit amount at opening
	r%= rate of interest per period =(annual rate/2) =8%/2=4%
	n= number of times deposit is compounded = number of years x no of times compounded in a year = 2 x 2 =4
	Future value = Present value x (1+ r%)^n
	Future value = 1000 x (1+ 4%)^4
	Future value = $1,169.85856
	Future value = $1,169.86
b.	8 percent compounded quarterly for two years
	8 percent compounded quarterly for two years, means 4 times compounded in a year for quarterly compounding , so in two years it will compounded for 8 times. Rate per quarterly be different as rate at which it will compounded quarterly = (annual rate/4) as for quarterly compounding it will be compounding 4 times in year .
	Future value = Ending balance in the account after 2 year =??
	Present value = $1000 deposit amount at opening
	r%= rate of interest per period =(annual rate/4) =8%/4=2%
	n= number of times deposit is compounded = number of years x no of times compounded in a year = 4 x 2 =8
	Future value = Present value x (1+ r%)^n
	Future value = 1000 x (1+ 2%)^8
	Future value = $1,171.65938
	Future value = $1,171.66
c.	8 percent compounded monthly for two years
	8 percent compounded monthly for two years, means 12 times compounded in a year for monthly compounding , so in two years it will compounded for 24 times. Rate per monthly be different as rate at which it will compounded monthly = (annual rate/12) as for monthly compounding it will be compounding 12 times in year .
	Future value = Ending balance in the account after 2 year =??
	Present value = $1000 deposit amount at opening
	r%= rate of interest per period =(annual rate/12) =8%/12=0.66666666%
	n= number of times deposit is compounded = number of years x no of times compounded in a year = 12 x 2 =24
	Future value = Present value x (1+ r%)^n
	Future value = 1000 x (1+ (8%/12))^24
	Future value = $1,171.88793
	Future value = $1,172.89
Please feel free to ask if anything about above solution in comment section of the question.