Q1 Written answer within 2hours plz

2 1+1 1. (8 marks) $100 is invested into Fund X which accumulates at a force of interest 5,- for OSIS 10.510,000 is invested into Fund Y which cams interest at an annual effective rate of interest i. At the end of year 10, the fund values in both funds are equal. (a) Calculate the fund value at the end of year 10; (b) Calculate i (6) Calculate the tund value in Fund Y at the end of year 3. 2. (16 marks) Ann takes out a $10,000 kan for 10 years and may repay the loan in the following two options: 1) Repay the loan with 10 equal annual payments at the end of each year with an effective annual interest rate of 10%; 2) Repay the loan with interest payments to the lender and level deposits into a sinking fund at the end of each year for 10 years. The sinking fund carns an annual effective interest rate of 12%. The lender charges an annual effective interest rate of i. The total payment (principal and interest) per ycar is the same for both options. (a) Find the amount of annual payment; (b) Find the principal paid and the interest paid during the first year in the first option: (c) Calculate the outstanding loan balance immediately after the payment in the first option: (d) Calculate i 3. (8 marks) A company must pay a benefit of $X to a customer in one year from now and $2X in twa years from now. To provide for the benefits, the company will buy a one-year bond with face value $1,000 and a two-year bond with face value $2.500 to exactly match the Isabilities. Both bonus have annual coupons, with an annual coupon rule of r for the one year bond and 1.5r for the two-year band. Determine the coupon rater. 2 1+1 1. (8 marks) $100 is invested into Fund X which accumulates at a force of interest 5,- for OSIS 10.510,000 is invested into Fund Y which cams interest at an annual effective rate of interest i. At the end of year 10, the fund values in both funds are equal. (a) Calculate the fund value at the end of year 10; (b) Calculate i (6) Calculate the tund value in Fund Y at the end of year 3. 2. (16 marks) Ann takes out a $10,000 kan for 10 years and may repay the loan in the following two options: 1) Repay the loan with 10 equal annual payments at the end of each year with an effective annual interest rate of 10%; 2) Repay the loan with interest payments to the lender and level deposits into a sinking fund at the end of each year for 10 years. The sinking fund carns an annual effective interest rate of 12%. The lender charges an annual effective interest rate of i. The total payment (principal and interest) per ycar is the same for both options. (a) Find the amount of annual payment; (b) Find the principal paid and the interest paid during the first year in the first option: (c) Calculate the outstanding loan balance immediately after the payment in the first option: (d) Calculate i 3. (8 marks) A company must pay a benefit of $X to a customer in one year from now and $2X in twa years from now. To provide for the benefits, the company will buy a one-year bond with face value $1,000 and a two-year bond with face value $2.500 to exactly match the Isabilities. Both bonus have annual coupons, with an annual coupon rule of r for the one year bond and 1.5r for the two-year band. Determine the coupon rater