Question

A microfinance company charges petty traders interest rate of 4 percent per month. what is the effective annual rate being charged the petty traders?

Answer 1

The effective annual rate (EAR) of a 4% monthly interest rate is calculated using compounding, resulting in a higher rate than simply multiplying by 12. The accumulation of interest is sensitive to changes in interest rates, exemplified by comparing 4% and 5% monthly rates, showing a substantial difference in the compounded annual result.

Step-by-step explanation:

To calculate the effective annual rate (EAR) charged by a microfinance company that applies a monthly interest rate of 4%, we need to account for the effect of compounding. This is because compounding can make the annual rate higher than simply multiplying the monthly rate by 12. The formula to calculate the EAR from a monthly rate is:

(1 + monthly interest rate)^number of periods per year - 1

So, plugging in the numbers for this scenario:

(1 + 0.04)^12 - 1 = (1.04)^12 - 1

Calculating this out will give the effective annual rate. As interest rates change, the accumulation of interest also changes. As an indication of how sensitive accumulation is to interest rates, consider that a slight increase to 5% per month would lead to an even higher EAR, demonstrating the maturity impact of higher rates.

Comparing the accumulation of interest for 4% and 5% monthly interest rates shows how quickly interest can grow due to compounding.

Answer 2

1.04% per annum

Explanation

е∧(0.04) = 1.04% per annum

Effective Annual Rate (EAR) is the actual rate since in this case, the interest rate is being compounded on the monthly basis. Using the formula where EAR is calculated by using the mathematical value of 'e' and then putting in the monthly rate as the power of 'e', we are able to achieve the EAR.