Question

Having recently inherited some money from a distant relative, you are considering investing the funds in financial assets. You are aware that financial assets exhibit four main attributes. List and discuss these attributes. In your answer give examples to explain your points. (Marks 4) (b) Tim is going to retire in 10 years. He is planning to build a retirement fund that he would like to receive at the end of 10 years from now. Company Y offers a package of two investment opportunities - C1 and C2. Tim will have to make separate investments in C1 for 10 years and C2 for 5 years. The investment in C1 should start now, however the investment in C2 will start in 6th year. Both investments (C1 and C2) will mature at the same time at the end of 10th year.

The details of the C1 and C2 investment plans are as follows:

Investment C1: The required investment at present is $80,000.00 which will go through 4 following phases (phase 1 to 4) in next 10 years. At the end of each phase the entire fund will automatically be rolled over to the next phase for re- investment. The investment will mature at the end of phase 4.

The 4 phases are as follows:

Phase 1: During the first 2 years the investment will earn 12% p.a. simple interest, then roll over to phase 2;

Phase 2: In the following 3 years the investment will earn 12% p.a. compounding monthly, then roll over to phase 3;

Phase 3: In the following 3 years the investment will earn 8% p.a. compounding annually, then roll over to phase 4;

Phase 4: The final 2 years of the investment will earn 10% return p.a. compounding daily. The investment matures at the end of phase 4.

Investment C2: This investment is spread over 5 years. It will commence in the 6th year of the 10 year investment plan. C2 requires an investment of $10,481.00 at the end of each quarter for 5 years, which will earn a 12% p.a. return compounding quarterly.

Both investments in C1 and C2 will mature at the end of the 10th year. How much, in total, will Tim accumulate from both investment opportunities at the end of 10th year? Explain why the returns from each investment are different. (Assume 1 year = 12 months = 52 weeks = 365 days).

Answer 1

Investment Plan C 1

Phase 1inital Investment = 80,000

Interest earned with simple interest @ 12% per annum

Phase 1 Time = 2 Years

Int = PTR

where P = principal T = time R = Rate of Interest
= $ 80000 * 2 * 12 %
= $ 19200
Total Balance at the end of Phase 2 = 80000 + 19200 = 99200

Phase 2 inital Investment = 99,200  time peroiod = 3 Years, compuding factor = monthly & rate of interest is 12%

A = P(1+r/n)^nt
A   =   final amount
P   =   initial principal balance
r   =   interest rate
n   =   number of times interest applied per time period
t   =   number of time periods elapsed

Final Amount = 99200 (1+ 0.12/12)^12*3

= 99200 (1+0.01)^36

= $ 99200 ( 1.01 ^ 36)
= $ 99200 * 1.4308
= $ 141932.26

Phase 3 inital Investment = 141,932.26 time peroiod = 3 Years, compuding factor = annually & rate of interest is 8%

A = P(1+r/n)^nt

=$ 141932.26 (1+ 0.08/1)^ 3 * 1

= $ 141932.26 ( 1 + 0.08) ^ 3
= $ 141932.26 ( 1.08 ^ 3)
= $ 141932.26 * 1.2597
= $ 178793.77

Phase 4 inital Investment = 178,793.77 time peroiod = 2 Years, compuding factor = daily & rate of interest is 10%

= $ 178793.77 (1+0.10/365)^ 2 * 365

= $ 178793.77 ( 1 + 0.000274) ^ 730
= $ 178793.77 ( 1.000274 ^ 730)
= $ 178793.77 * 1.2214
= $ 218373.22

Investment Plan C 2

Particulars	Amount
Cash Flow	$          10,481.00
Int Rate per quarter 12%/4	3.000%
Periods 5 Years * 4 quarters	20

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 10481 * [ [ ( 1 + 0.03 ) ^ 20 ] - 1 ] / 0.03
= $ 10481 * [ [ ( 1.03 ) ^ 20 ] - 1 ] / 0.03
= $ 10481 * [ [1.8061] - 1 ] / 0.03
= $ 10481 * [0.8061] /0.03
= $ 281628.4

Total Value Investments = 178793.77 +281628.4

= 460422.81