Question

You Invested summer earnings into an annuity from which you can draw expenses while in college. if you withdraw $1200 each month for 9 month of school, how much do you need to invest in an account, earning 6% per year, compounded semi-annually in order to cover your expenses

Answer 1

Step 1 :	Calculation of effective monthly rate
	Six monthly rate = 6%/2 =3%
	3% =(1+r)^6
	r =0.493862%
Step 2 :	Calculation of Amount need to be invested
	Present Value Of An Annuity
	= C*[1-(1+i)^-n]/i]
	Where,
	C= Cash Flow per period
	i = interest rate per period =0.493862%
	n=number of period =9
	= $1200[ 1-(1+0.00493862)^-9 /0.00493862]
	= $1200[ 1-(1.00493862)^-9 /0.00493862]
	= $1200[ (0.0434) ] /0.00493862
	= $10,538.07