Question

Can you solve for the following scenario. Thank you!

s Rachel's 30 birthday. Five years ago, Rac hel opened a brokerage account when her grandmsother gave her $25,000 for her 25 birthday. Rachel added $2,000 to this account n her 26 birthday, $3,000 on her 27e birthday, $4,000 on her 28 birthday, and $5,000 on her 29h birthday. Rachel's goal is to have $400,000 in the account by her 40 birthday ing today, she plans to contribute a fixed amount to the account each year on her birthday. She will make 11 contributions, the first one will occur today, and the final contrib occur on her 40 birthday. Complicating things somewhat is the fact that Rachel plans to withdraw $20,000 from the account on her 35 birthday to finance the down payment home. How large does each o these contrib ut ons have to be r Rachel to reach her goal? Assume the accon t has earned and will continue to earn an effective return of 12% a 国画 IT

Answer 1

			Future Value(FV) of Cash Flow on40th Birthday (at end of 15th Year):
			FV=(Cash Flow)*((1+i)^(15-N))
			i=Interest Rate=12%=0.12
			N=Year of Cash Flow
			Assume 25th Birthday as 0 year
			CASH FLOW IS GIVEN BELOW
			N	A	B=A*(1.12^(15-N)	C	D=B*(1.12^(15-N)
			Year	Cash flow	FV of Cash Flow	Annual Savings	Future Value of Savings
		25th birthday	0	$25,000	$136,839
		26th birthday	1	$2,000	$9,774
		27th birthday	2	$3,000	$13,090
		28th birthday	3	$4,000	$15,584
		29th birthday	4	$5,000	$17,393
	TODAY	30th birthday	5		$0	$11,743.93	$36,475
		31st birthday	6		$0	$11,743.93	$32,567
		32nd birthday	7		$0	$11,743.93	$29,078
		33rd birthday	8		$0	$11,743.93	$25,962
		34th birthday	9		$0	$11,743.93	$23,180
		35th birthday	10	($20,000)	($35,247)	$11,743.93	$20,697
		36th birthday	11		$0	$11,743.93	$18,479
		37th birthday	12		$0	$11,743.93	$16,499
		38th birthday	13		$0	$11,743.93	$14,732
		39th birthday	14		$0	$11,743.93	$13,153
		40th birthday	15		$0	$11,743.93	$11,744
				SUM	$157,434	SUM	$242,566
							TOTAL FV	$400,000	(157434+242566)
			SUM of Future Values	$157,434
			Required amount (Goal)	$400,000
			Additional amount required	$242,566	(400000-157434)
			Amount of each of 11 annual contributions required beginning today	$11,743.93	(Using PMT Function of excel with Rate=12%, Nper=11, Fv=-242566)