calculate the nominal interest per annum if the effective rate was 11.4% p.a compounded half yearly for 5 years

ten periods at .057 per period

1.057^10 = 1.74

for five one year compoundings:
x^5 = 1.74
5 log x = log 1.74 = .24055
log x = .04810984
10^log x = x = 1.117
or 11.7 %

To calculate the nominal interest per annum when the effective rate is given, you can use the formula:

Nominal Interest Rate (per annum) = ((1 + Effective Rate for one period) ^ Number of compounding periods) - 1

In this case, the effective rate is 11.4% per annum compounded half yearly, which means there will be two compounding periods per year.

First, convert the effective rate to a decimal form: 11.4% = 0.114.

Next, calculate the effective rate for one period using the formula:

Effective Rate for one period = ((1 + Effective Rate for one year) ^ (1 / Number of compounding periods)) - 1

Effective Rate for one period = ((1 + 0.114) ^ (1 / 2)) - 1 = ((1 + 0.114) ^ 0.5) - 1

Now, substitute these values into the formula for the nominal interest rate:

Nominal Interest Rate (per annum) = ((1 + 0.114 ^ 0.5) - 1) ^ 2 - 1

Calculate the result:

Nominal Interest Rate (per annum) = ((1.05792586089) - 1) ^ 2 - 1

Nominal Interest Rate (per annum) = 0.12234506, or 12.23% per annum compounded semi-annually.

Therefore, the nominal interest rate per annum is approximately 12.23% compounded semi-annually.