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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%.

### 1 Answer by Expert Tutors

Joseph C. | Joseph, Trilingual instructor, Paso Robles, CAJoseph, Trilingual instructor, Paso Robl...
5.0 5.0 (105 lesson ratings) (105)
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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%