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You manage an investment portfolio.
On August 1, 2018, a new client invested $50,000 into your portfolio. Three months (i.e., 1/4 of one year) later the client withdrew $10,000 and the account balance immediately following this withdrawal was $41,000. Six months (i.e., 1/2 of one year) after the withdrawal you issued a $1,500 dividend to the client and, at the client's instruction, the dividend was immediately reinvested in the portfolio. There was no other activity in the account and on August 1, 2019 the balance in the account was $43,050.
Part 1) Write an equation that would solve for the dollar-weighted return. Please make sure your equation is easy to read (including any exponents).
Part 2) What is the annualized time-weighted return (i.e., geometric return or CAGR)? Please show your work.
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