Nominal Rate of Interest: 9.9% p.a.




To calculate the effective rate of interest when interest is compounded monthly, we need to understand the concept of nominal rate and effective rate.

Nominal Rate of Interest:
The nominal rate of interest is the stated or advertised rate of interest on a loan or investment. It is expressed as a percentage per annum (p.a.). In this case, the nominal rate of interest is 9.9% p.a.

Effective Rate of Interest:
The effective rate of interest takes into account the compounding effect and reflects the true cost or return on a loan or investment. It is the actual rate at which interest is earned or paid after considering the compounding period. The effective rate is always higher than the nominal rate.

Calculation:
To calculate the effective rate of interest, we need to use the formula:

Effective Rate = (1 + i/n)^n - 1

Where:
i = nominal rate of interest (in decimal form)
n = number of compounding periods per year

In this case, the nominal rate of interest is 9.9% p.a., which is equivalent to 0.099 in decimal form. As the interest is compounded monthly, the number of compounding periods per year is 12.

Substituting the values into the formula:

Effective Rate = (1 + 0.099/12)^12 - 1

Calculating this expression, we get:

Effective Rate = (1.00825)^12 - 1

Effective Rate = 1.104713 - 1

Effective Rate = 0.104713

Therefore, the effective rate of interest when the nominal rate is 9.9% p.a. with monthly compounding is approximately 10.47% p.a.

Explanation:
The effective rate of interest is higher than the nominal rate because interest is compounded monthly. Compounding means that the interest earned or paid in each period is added to the principal, and subsequent interest calculations are based on the new higher balance.

So, in this case, the effective rate of interest takes into account the compounding effect of monthly compounding, resulting in a higher overall rate of interest over the course of a year.

Conclusion:
The effective rate of interest when the nominal rate is 9.9% p.a. with monthly compounding is approximately 10.47% p.a. It is important to consider the effective rate when comparing different loan or investment options, as it provides a more accurate representation of the true cost or return.