Question

Problem 4 Company ABC has an investment stream, S(n), over 2 years that can be represented as a continuous first degree polynomial function as given in the below figure for year 1 and year 2 (1) If a continuously compounded interest is applied to the instantaneous cash flow investment stream, determine the future worth of the investment at the end of year 6 Investment Stream $1,000 /year Investment Stream, $/year Time, years (2) If the investment stream was abruptly discontinued at the end of year 1, how much accumulated interest is lost from the future value after 6 years compared to Part 1? Note, the accumulated interest should not include the investment stream amount (Hint: I-F-T) For both Part 1 and Part 2 of Problem 4, use a nominal interest rate of 15%/year

Answer 1

Sol. Part 1: In Year 0: Investment is $1000.00, in Year 1: $500.00 and in Year 2: No investment thus Future Value will be calculated @15% rate p.a. but as it is continuous compounding which means daily, the formula on time line should be: $1000*(1+0.15/365)^7*365 = $2857.03 plus $500*(1+0.15/365)^6*365 = $1229.57 thus total value at the end of Six years should be 4086.60.

Sol Part 2: In Year 0: Investment is $1000.00 then no investment in the future.  Future Value will be calculated @15% rate p.a. but as it is continuous compounding which means daily, the formula on time line should be: $1000*(1+0.15/365)^7*365 = 2857.03. Thus on account of not investing $500.00 in Year 1 the loss of accumulated interest will be $1229.57-$500.00= $729.57 only.