What is the nominal rate per annum when interest is payable half-yearly that would be given an effective rate of 10% per annum?

To find the nominal rate per annum when interest is payable half-yearly, we need to use the formula for the effective annual rate (EAR), which is:

EAR = (1 + i/n)^(nt) - 1

where:

• EAR is the effective annual rate
• i is the nominal interest rate
• n is the number of compounding periods per year
• t is the number of years

In this case, we know that the EAR is 10% (or 0.10 when expressed as a decimal), n is 2 (since interest is payable half-yearly), and t is 1 (since we're looking for the annual rate). We can plug these values into the formula and solve for i:

0.10 = (1 + i/2)^(2*1) - 1

Solving this equation for i will give us the nominal rate per annum.

First, add 1 to both sides of the equation:

1.10 = (1 + i/2)^2

Then, take the square root of both sides:

sqrt(1.10) = 1 + i/2

Subtract 1 from both sides:

sqrt(1.10) - 1 = i/2

Finally, multiply both sides by 2 to solve for i:

2 * (sqrt(1.10) - 1) = i

This will give you the nominal rate per annum when interest is payable half-yearly that would give an effective rate of 10% per annum.