Calculation of Nominal Rate of Interest per Annum with Quarterly Compounding

Effective Rate of Interest
- The effective rate of interest is the actual rate of interest earned on an investment over a certain period of time, taking into account the effects of compounding.
- In this problem, the effective rate of interest is given as 12% per annum.

Compounding Frequency
- Compounding refers to the process of earning interest on interest.
- The frequency of compounding determines how often interest is added to the principal amount.
- In this problem, the interest is compounded quarterly, which means that interest is added to the principal every three months.

Formula for Effective Rate of Interest
- The formula for calculating the effective rate of interest with quarterly compounding is:
(1 + r/4)^4 - 1
where r is the nominal rate of interest per annum.

Substitution of Values
- Substituting the given value of the effective rate of interest into the formula, we get:
(1 + r/4)^4 - 1 = 0.12

Simplification and Solving for r
- Simplifying the equation, we get:
(1 + r/4)^4 = 1.12
Taking the fourth root of both sides, we get:
1 + r/4 = 1.0291
Subtracting 1 from both sides, we get:
r/4 = 0.0291
Multiplying both sides by 4, we get:
r = 0.1164 or 11.64%

Nominal Rate of Interest per Annum
- Therefore, the nominal rate of interest per annum with quarterly compounding is 11.64%.

Note: The nominal rate of interest is the stated rate of interest without taking into account the effects of compounding.