Question

I have $ 10,000 USD. You can invest in the following options at any time:

Investment A: Each dollar invested now yields 0.08 dollar within one year from today and 1.25 three years after this time.

Investment B: Each dollar invested now yields 0.15 dollar within one year from today and 1.10 two years after this time.

Investment C: Each dollar invested now yields 1.40 within three years after this moment.

Consider that we are at the beginning of year 1.

Cash that is not invested can be allocated to the stock market funds during each year, where it yields 4% interest per year.

You can place as much as $ 5,000 USD in each investment at any point of time.

Set up a model that maximizes my cash within six years (that is, the amount of money I will have available at the beginning of year 7), solve it and specify the maximum amount that I could receive.

Answer 1

I have $ 10,000 USD. You can invest in the following options at any time:

• Investment A: Each dollar invested now yields 0.08 [8%] dollar within one year from today and 1.25 [125%] three years after this time.
• Investment B: Each dollar invested now yields 0.15 [15%] dollar within one year from today and 1.10 [110%] two years after this time.
• Investment C: Each dollar invested now yields 1.40 [1.40] within three years after this moment.

Consider that we are at the beginning of year 1.

• Cash that is not invested can be allocated to the stock market funds during each year, where it yields 4% interest per year.
• You can place as much as $ 5,000 USD in each investment at any point of time.

Set up a model that maximizes my cash within six years (that is, the amount of money I will have available at the beginning of year 7), solve it and specify the maximum amount that I could receive.

Solution:

Yr.	Investment -A			Investment -B			Investment -C			Stock Investment
	Rate of Interest	Compounded Rate of Interest	Amount to be received at year 7	Rate of Interest	Compounded Rate of Interest	Amount to be received at year 7	Rate of Interest	Compounded Rate of Interest	Amount to be received at year 7	Rate of Interest	Compounded Rate of Interest	Amount to be received at year 7
1	800	800	10800	1500	1500	11500	0	0	10000	400	0	10000
2	0	800	10800	0	1500	11500	0	0	10000	400	400	10400
3	0	800	10800	11000	12500	22500	14000	14000	24000	400	800	10800
4	12500	13300	23300		12500	22500		14000	24000	400	1200	11200
5		13300	23300		12500	22500		14000	24000	400	1600	11600
6		13300	23300		12500	22500		14000	24000	400	2000	12000
7		13300	23300		12500	22500		14000	24000	400	2400	12400

Interpretation:

• Investment-C will yield highest return [24000] followed by Investment-A [23300] and lest return yielding investment is Investment-B [22500].
• The investment on Stock market would yield the least investment.
  • Hereby we are reject investment on Stock option.

Hence, we are considering investment on Investment-A and Investment-C options with each $5000 USD. [Given Condition: You can place as much as $ 5,000 USD in each investment at any point of time]