(d) Given: L = $10,000, M = $1000, R = 4%, find your savings in the plan after the first 24 months end. (2 mark) (e) Determine the lump sum received after you completed the whole plan.A nancial advisor suggests an investment plan for your consideration. > Your one-time initial investment is $L. >> You put a xed monthly contribution of $114 to the plan for 24 months. You will contribute to the plan on the last date of each month. 3P The plan will pay you an annual interest rate of 12% compounded monthly during these 24 months. The interests will be deposited into your plan on the last date of each month. '5 After 24 months of continuous investment, you can stop the monthly contributions and keep the money in the plan for additional [20 months. The plan will pay you an annual interest rate of (R +l )% compounded monthly during this period. > When the investment plan is completed, you will receive an extra 5% of your total savings as a bonus. Let Sn be the amount of money saved in the plan at the end of the n\"' month, following the nltl monthly contribution. You start to contribute on the last date of the rst month and pay the last monthly contribution at the end of the 24''1 month. (a) Write down a recurrence relation for $1, 32, 53 in terms of L, M, and R (2 marks) (b) Propose a recurrence relation to express 3,; in terms of 3,14, L, M, and R. (I mark) (c) Use the method of undetermined coetct'ents to your proposed relation in (b) to nd explicit formula for Sn in terms of L. M, and R