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an interest rate of 1% per month is the same as: a) nominal 3% per quarter compounded monthly. b) effective 12.683% per year compounded monthly. c) nominal 12% per year compounded monthly. d) all of the above.

User Alen Smith
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1 Answer

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Final answer:

The interest rate of 1% per month is equivalent to approximately 12.68% per year compounded monthly, which applies to all of the given options.

Step-by-step explanation:

The interest rate of 1% per month can be converted to an equivalent annual rate compounded monthly by using the formula:

Annual Interest Rate = (1 + Monthly Interest Rate)^12 - 1

So, let's calculate the equivalent annual interest rate for each given option:

a) Nominal 3% per quarter compounded monthly:

Monthly Interest Rate = 3% / 3 = 1% = 0.01

Annual Interest Rate = (1 + 0.01)^12 - 1 = 12.68% (approximately)

b) Effective 12.683% per year compounded monthly:

This option is already the equivalent annual interest rate.

c) Nominal 12% per year compounded monthly:

Monthly Interest Rate = 12% / 12 = 1% = 0.01

Annual Interest Rate = (1 + 0.01)^12 - 1 = 12.68% (approximately)

Based on the calculations, options a, b, and c all have an equivalent annual interest rate of approximately 12.68%. Therefore, the correct answer is d) all of the above.

User Wolfgang Adamec
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