Nominal Rate of Interest and Effective Rate of Interest

The nominal rate of interest is the stated rate of interest that is mentioned in a financial contract or agreement. It is usually expressed as an annual percentage rate (p.a.). On the other hand, the effective rate of interest is the actual rate of interest that is earned or paid after taking into account the compounding of interest over a given period of time.

Compounding

Compounding refers to the process of earning interest on both the initial principal amount and the accrued interest. In the case of monthly compounding, the interest is calculated and added to the principal every month.

Calculating Effective Rate of Interest

To calculate the effective rate of interest, we need to consider the compounding period and the nominal rate of interest. In this case, the compounding period is monthly and the nominal rate of interest is 9.9% p.a.

Formula for Effective Rate of Interest:
Effective Rate of Interest = (1 + (Nominal Rate/Number of Compounding Periods))^Number of Compounding Periods - 1

Calculation:
- Nominal Rate of Interest = 9.9% p.a.
- Number of Compounding Periods = 12 (since interest is compounded monthly)

Using the formula mentioned above, we can calculate the effective rate of interest:

Effective Rate of Interest = (1 + (9.9%/12))^12 - 1

Result:
The effective rate of interest, when the nominal rate of interest is 9.9% p.a. and interest is compounded monthly, is approximately 10.46% p.a.

Explanation:
The effective rate of interest takes into account the impact of compounding on the nominal rate. In this case, the nominal rate of 9.9% p.a. is compounded monthly, which results in an effective rate of interest of approximately 10.46% p.a. This means that if you were to invest or borrow money at a nominal rate of 9.9% p.a. with monthly compounding, you would actually earn or pay interest at a rate of 10.46% p.a.