Question

Suppose a recent college graduate's first job allows her to deposit $200 at the end of each month in a savings plan that earns 9%, compounded monthly. This savings plan continues for 11 years before new obligations make it impossible to continue. If the accrued amount remains in the plan for the next 15 years without deposits or withdrawals, how much money will be in the account 26 years after the plan began? (Round your answer to the nearest cent.)

Answer 1

Step 1:	Future value of an ordinary annuity at the end of 11 th year
	c= Cash Flow	200
	i= Interest Rate =9%/12 =	0.0075
	n= Number Of Periods =11*12 =	132
	Future Value of an Ordinary Annuity
	= C*[(1+i)^n-1]/i
	Where,
	C= Cash Flow per period
	i = interest rate per period
	n=number of period
	= $200[ (1+0.0075)^132 -1] /0.0075
	= $200[ (1.0075)^132 -1] /0.0075
	= $200[ (2.6813 -1] /0.0075]
	= $44,834.97
Step 2 :	Future value of amount $44834.97 after 15 years compunding monthly
	PV	44,834.97
	r =9%/12	0.75%
	n =15*12 =	180
	FV= PV*(1+r)^n
	Where,
	FV= Future Value
	PV = Present Value
	r = Interest rate
	n= periods in number
	= $44834.9675*( 1+0.008)^180
	=44834.9675*3.83804
	= $172078.55
Amount at the end of year 26 would be = $172078.55