Q5 Written answer within 2hours plz

On October 1, 2019, Julia opened an account with a balance of S100,000. On December 1, 2019, she deposited 59,000 to the account. On April 1, 2020, SX was added to the account On September 1, 2020, sbe withdrew S12,000. The final balance on October 1, 2020 was 5112.000. Calculate $X if the annual effective interest rate is 5% computed using the dollar-weighted method 5. (15 marks) Sunglasses from Brand A last 6 years and cost $3,000 per pair Sunglasses from Brand B last 10 years and cost SX per pair. Find the value of X with an annual effective interest rate of 7% at which a user would be indifferent between the two brands if the user needs sunglasses for eye protection for 25 years. Assume users are loyal and will not change the brand of the sunglasses once she be purchases the first pair of the sunglasses from a brand. 6. (15 marks) An annuity-immediate has level annual payments for n years. The average time of the payments using the method of equated time is 10 years. The annual effective rate of interest 1 is equal to 10% (+1) (a) Calculate the value of n (hint: 1+2+3++ : 2 (b) Based on the result from (a), calculate (la): (c) Determine the Macaulay duration of the payments. (d) If -3 determine the convexity of the payments. On October 1, 2019, Julia opened an account with a balance of S100,000. On December 1, 2019, she deposited 59,000 to the account. On April 1, 2020, SX was added to the account On September 1, 2020, sbe withdrew S12,000. The final balance on October 1, 2020 was 5112.000. Calculate $X if the annual effective interest rate is 5% computed using the dollar-weighted method 5. (15 marks) Sunglasses from Brand A last 6 years and cost $3,000 per pair Sunglasses from Brand B last 10 years and cost SX per pair. Find the value of X with an annual effective interest rate of 7% at which a user would be indifferent between the two brands if the user needs sunglasses for eye protection for 25 years. Assume users are loyal and will not change the brand of the sunglasses once she be purchases the first pair of the sunglasses from a brand. 6. (15 marks) An annuity-immediate has level annual payments for n years. The average time of the payments using the method of equated time is 10 years. The annual effective rate of interest 1 is equal to 10% (+1) (a) Calculate the value of n (hint: 1+2+3++ : 2 (b) Based on the result from (a), calculate (la): (c) Determine the Macaulay duration of the payments. (d) If -3 determine the convexity of the payments