If the effective rate is 12.68% per annum, find the nominal rate per annum if the compounding occurs half-yearly.

Answer 1

To convert the effective rate to the nominal rate with semi-annual compounding, we use the formula:

(1 + Nominal Rate / 2)^2 = 1 + Effective Rate

(1 + Nominal Rate / 2)^2 = 1 + 0.1268
(1 + Nominal Rate / 2)^2 = 1.1268

Taking the square root of both sides:

1 + Nominal Rate / 2 = √1.1268
1 + Nominal Rate / 2 ≈ 1.063106

Subtracting 1 from both sides:

Nominal Rate / 2 ≈ 0.063106

Multiplying by 2:

Nominal Rate ≈ 0.126212

Therefore, the nominal rate per annum with semi-annual compounding is approximately 12.62%.