PPlease address the following questions giving precisely. Thank you

A member of a pensions savings scheme invests f1,200 per annum in monthly instalments. in advance. for 20 years from his 25" birthday. From the age of 45. the member increases his investment to $2,400 per annum. At each birthday thereafter the annual rate of investment is further increased by f.100 per annum. The investments continue to be made monthly in advance for 20 years until the individual's 65th birthday. (i) Calculate the accumulation of the investment at the age of 65 using a rate of interest of 6% per annum effective. [6] At the age of 65, the scheme member uses his accumulated investment to purchase an annuity with a term of 20 years to be paid half-yearly in arrear. At this time the interest rate is 5% per annum convertible half-yearly. (ii) Calculate the annual rate of payment of the annuity. [31 (Hi) Calculate the discounted mean term of the annuity, in years, at the time of purchase. [3] [Total 12] A bank offers a customer two different repayment options on a loan of f50,000 as follows: Option 1 - level instalments of capital and interest are paid annually in arrear over a period of 20 years. Option 2 - over the 20-year term the customer pays only interest on the loan, annually in arrear at a rate of 5.5% per annum with the whole of the capital amount payable at the end of the term. The customer will take out a separate savings policy which involves making monthly payments in advance such that the proceeds will be sufficient to repay the loan at the end of its term. The payments into the savings policy accumulate at a rate of interest of 4% per annum effective. (1) Determine the effective rate of interest per annum that would be paid by the customer on the loan under Option 1, given that the level anmal instalment on this loan is f4,012.13. [3] (ii) Determine the annual effective rate of interest paid by a customer under Option 2. [7] [Total 10]