If an installment plan quotes a monthly interest rate of 4%, the effective annual/yearly interest rate would be __________. 4%Between 4% and 48%48%More than 48%
Question
If an installment plan quotes a monthly interest rate of 4%, the effective annual/yearly interest rate would be __________. 4%Between 4% and 48%48%More than 48%
Solution
The effective annual interest rate would be More than 48%.
Here's why:
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The monthly interest rate is 4%.
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To find the annual interest rate, you might think to simply multiply the monthly rate by 12 (the number of months in a year). This would give you 48%.
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However, this calculation assumes that the interest is not compounded. In reality, interest is usually compounded, meaning that each month, you're charged interest on the original amount plus any accumulated interest.
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Therefore, the effective annual interest rate is actually higher than 48% when you take into account the effects of compounding.
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The formula to calculate the effective annual interest rate is (1 + i/n)^(nt) - 1, where i is the nominal interest rate (4% or 0.04 in this case), n is the number of compounding periods per year (12 in this case), and t is the number of years (1 in this case).
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Plugging these values into the formula gives you an effective annual interest rate of approximately 60.1%.
So, the correct answer is "More than 48%".
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