Question

Slight challenge question with a twist on the return measurement problems. If you understand how to set up an equation to solve for the annualized dollar-weighted return you should be able to solve this question. Two years ago you opened a new investment account and invested $9,000 at that time. Six months later you withdrew $1,000, and then one year after that withdrawal you invested an additional $2000. There were not other deposits and withdrawals, and today the balance $X. If the annualized dollar-weighted return was 8%, what is X? Round and express your answer to the nearest dollar.

Answer 1

		Consider Sixmonthly period
		Period	Cash flow
		0	($9,000)
		1	$1,000
		3	($2,000)
		4	X
		Annualized Dollar weighted Return	8%
		Return for six month period =(1.08^(1/2))-1	3.92%
		(-9000+(1000/1.0392)-(2000/(1.0392^3)+X/(1.0392^4))=0
		X/(1.0392^4)=9000-962.28+1782.10=	9819.82		962.2787	1782.102
		X=9816.45*(1.08^2)=	11453.83805
		X=	$11,453.84
		Value of X innearest dollar	$11,454
		Check;
		Period	Cash Flow
		0	($9,000)
		1	$1,000
		2	$0
		3	($2,000)
		4	$11,454
		InternalRate of return for 6 monthly period	4%	(Using IRR function over cash flow
		Annualized Return	8%