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Suppose you want to earn an effective rate of 16% and you are looking at an account that compounds on a monthly basis. What APR must they pay?

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Effective annual rate = (1 + Annual percentage rate / compounding frequency)^{compounding frequency} - 1

16% = (1 + Annual percentage rate / 12)¹² - 1

1.16 = (1 + Annual percentage rate / 12)¹²

(1.16)^{(1 / 12)} = (1 + Annual percentage rate / 12)

1.012445 = (1 + Annual percentage rate / 12)

0.012445 = Annual percentage rate / 12

Annual percentage rate = 12 * 0.012445

Annual percentage rate(APR) = 14.9342%

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