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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%

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Solution

The effective annual interest rate would be More than 48%.

Here's why:

  1. The monthly interest rate is 4%.

  2. 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%.

  3. 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.

  4. Therefore, the effective annual interest rate is actually higher than 48% when you take into account the effects of compounding.

  5. 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).

  6. 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%".

This problem has been solved

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