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A classical musician inherits $3,000. She currently has $4850 of credit card debt,

 on which she is charged an annual yield of 21%. Putting $3,000 toward this would cut that debt to $1,850. Calculate the annual rate of return if she does this. Round, if necessary, to the nearest 0.1%.

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Joseph C. | Joseph, Trilingual instructor, Paso Robles, CAJoseph, Trilingual instructor, Paso Robl...
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Point 1: The term "annual yield" is misused here. Annual yield generally refers to the rate paid to a depositor by a financial institution. The term is not generally used in reference to debt.

Point 2: The term "return on investment" is used to describe profit on an investment, not a reduction in expenses.

Point 3: No time frame is given here, so we must assume one year

Point 4: No payment date is given, so, for maximum impact, we must assume 1 January

Point 5: An annual percentage of 21% implies simple interest, an uncommon method for most loans, with the exception of real estate loans.

That being said, $4850 carried at 21% for one year, would cost $4850 x 0.21 = $1,018.50

If a payment of $3,000 is made on 1 January, and the balance carried for the entire year, then $4850 - 3000 = $1850 x 0.21 = $388.50

The expense reduction will be $1018.50 - 388.50 = $630.00

The "return on investment" will be $630.00 รท $3000 = 0.21 = 21%