A Financial Advisor Suggests An Investment Plan For Your Consideration Your One Time Initial Investment Is L You Put 1 (293.46 KiB) Viewed 59 times
A Financial Advisor Suggests An Investment Plan For Your Consideration Your One Time Initial Investment Is L You Put 2 (24.56 KiB) Viewed 59 times
A financial advisor suggests an investment plan for your consideration. Your one-time initial investment is $L. You put a fixed monthly contribution of $M to the plan for 24 months. You will contribute to the plan on the last date of each month. The plan will pay you an annual interest rate of R% compounded monthly during these 24 months. The interests will be deposited into your plan on the last date of each month. After 24 months of continuous investment, you can stop the monthly contributions and keep the money in the plan for additional 120 months. The plan will pay you an annual interest rate of (R+1)% 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 S be the amount of money saved in the plan at the end of the nth month, following the nth monthly contribution. You start to contribute on the last date of the first month and pay the last monthly contribution at the end of the 24th month. (a) Write down a recurrence relation for S1, S2, S3 in terms of L, M, and R (2 marks) (b) Propose a recurrence relation to express Sn in terms of Sn-1, L, M, and R. (1 mark) (c) Use the method of undetermined coefficients to your proposed relation in (b) to find an explicit formula for Sn in terms of L, M, and R.
(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.
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