Solve showing all the steps

Describe the characteristics of Government Bills. (3] Describe the characteristics of: an interest-only loan (or mortgage ); and (b) a repayment loan ( or mortgage). [4] A loan is to he repaid by an annuity payable annually in arrear. The annuity starts at a rate of $300 per annum and increases each year by $30 per annum. The annuity is to be paid for 20 years. Repayments are calculated using a rate of interest of 7% per annum effective. Calculate: The amount of the loan. [3] (ii) The capital outstanding immediately after the 5" payment has been made. [2] (iii) The capital and interest components of the final payment. (2] [Total 7] (i) Explain what is meant by the "no arbitrage" assumption in financial mathematics. 12] An investor entered into a long forward contract for f100 nominal of a security eight years ago and the contract is due to mature in four years' time. The price per (100 nominal of the security was 194.50 eight years ago and is now f143.00. The risk-free rate of interest can be assumed to be 5% per annum effective throughout the contract. (ii) Calculate the value of the contract now if it were known from the outset that the security will pay coupons of by two years from now and $10 three years from now. You may assume no arbitrage. [5] [Total 7]A life insurance company is issuing a single premium policy which will pay out f20,000 in twenty years time. The interest rate the company will earn on the invested funds over the first ten years of the policy will be 4% per annum with a probability of 0.3 and 6% per annum with a probability of 0.7. Over the second ten years the interest rate earned will be 5% per annum with probability 0.5 and 6% per annum with probability 0.5. (1) Calculate the premium that the company would charge if it calculates the premium using the expected annual rate of interest in each ten year period. (2] (Hi) Calculate the expected profit to the company if the premium is calculated as in (1). The rate of interest in the second ten year period is independent of that in the first ten year period. [3] (iii) Explain why, despite the company using the expected rate of interest to calculate the premium, there is a positive expected profit. 12] (iv) By considering each possible outcome in (ii): (a) Find the range of possible profits. (b) Calculate the standard deviation of the profit to the company. [7] [Total 14]